Here's a few that you can do, including the one I outlined over there. Each drill has its title, rules, some background info that explains what the drill's trying to accomplish, and a list of variations on the drill you can also.
A note on the terminology: the player the drill is focusing on will be called “hero”. The human opponents in the drill will be called “villains”. Most of these drills will not work if bots are used instead of real villains, although I will point out where a bot will suffice.
Drill 1: “AA Boxing, with Reach”
Hero picks Caitlyn, Villain picks Lucian. Runes set to health regen and armor, no AD. Masteries set to defensive and support, no damage. Both players start with a Doran's Shield and one potion. No abilities are allowed, don't even spend the skill points. Auto attacks only.
Lane against each other in the bottom lane for nine waves (minions that arrive in the 10th wave, arriving at 6:30 may not be shot, but both players may still shoot minions that were there from the previous wave). Hero scores one point for every CS Villain missed, and vice versa. For every AA Hero (as Caitlyn) landed on Villain (Graves), Hero scores one point. For every attack Villain lands on Hero, he scores two points. Most points at the end of the last legal wave wins.
Background: Basic laning in LoL is like a boxing match. You can win by knockout, or on points if you couldn't kill the other guy. Imagine if there were targets that lit up in the boxing ring that the boxers could punch for points, and that the other boxer can capitalize on by punching his opponent while he's distracted by the target.
ADC matchups come in three categories: you have more AA range, you have the same AA range, or you have less AA range. The goal here is to maximize AA harass while not missing any CS. By forcing an uneven matchup where one champ has a range advantage, both players will need to learn to cope with this. The Villain player will need to be a step ahead and plan to safely walk up to the longer range champion to shoot them. The Hero player will need to recognize her range sweet spot and make sure that her opponent doesn't creep out of it while she's busy shooting creeps. Both players will need to attack often and still CS at a fast pace, lest they be pushed to tower and fall far behind in our little game.
Reverse It: Hero plays Graves, scoring 2 points per auto, and Villain plays Caitlyn, scoring one point per auto.
Any ADC You Like: Graves and Caitlyn were chosen because of the range difference, but players should eventually work out both playing as and playing against all ADCs they are likely to see, to get used to everyone's attack animations and whatnot.
Bring a GUN to a Gunfight: Players no longer score points for landing auto attacks, but abilities are now allowed, along with their choice of items, runes, and masteries. Players can win either by scoring a kill, or by being ahead on cs after nine waves.
Drill 2: “Hookshot Hell”
Hero picks the ADC of their choice, two Villains pick Blitzcrank and Thresh. ADC is free to choose any runes, masteries, or items. Villains may only take sustain, such as mana and health regen. No cooldown reduction is allowed, except for the mastery page. The Villains each take Heal and Clarity. The Villains should have voice chat, be in the same room, or have some way to communicate where the Hero can't hear them.
Hero lanes alone against two Villains in the bottom lane. Hero must take at least 5 minions per wave, or the Villains “win”. The Villains also “win” automatically by landing a hook (Rocket Grab or Death Sentence) on the Hero. If a “win” is scored, do not end the drill; let the Hero return to CSing and continue until the clock strikes 7 minutes. The Villains are not allowed to move past the Hero's furthest forward minion. Imagine a line, parallel to the river, that passes through the Hero's front minion. The Villains are offside if they pass it, and are not allowed to do anything other than retreat back onside if they are in front of it. The Hero wins if the clock strikes 7 minutes without the Villains winning. Villains are only allowed to harm the hero with their hooks, but may do whatever they like to the minion wave, provided they stay onside.
It's quite a problem for newer ADCs to deal with hard engage supports. The fact that they're up against skills that will probably lose them the lane if they're landed make many ADCs play over-passive, and lose anyway as a result. This drill is designed to teach the ADC the limits of hook supports and how to deal with them. The Hero will need to outwaveclear the Villains, gaining a minion advantage in the form of disposable “shields” that can block hooks, all the while CSing properly. Since the villains are communicating, the Hero will also need to deal with the Villains' tricks, such as being prepared for a hook coming right through the space where a minion was a second ago, up until the other Villain killed it. Finally, the Hero will have to develop “bait” skills, trying to entice the Villains to throw their hooks and miss, earning the Hero a significant reprieve in lane that he can use to advantage.
The Flash Exception: Villains may now take Flash. They are allowed to use their hooks when they are offside, provided the flash spell was used to cross the offside line and the hook is thrown immediately. Hit or miss, the Villains must immediately retire back onside, so they are not past the Hero's forwardmost minion.
I HATE Cheese: The Villains, if they so choose, may also take Smite. They can use these to instantly clear minions to create a hook path.
Those Aren't Even Hooks: Villains can now play other support champions that have engage in different forms, such as Leona or Annie. Record any hard CC skill (where the victim cannot move) that lands as a “win”.
WTF Troll Support: Villains may take any champion, and not only supports. Any Champion with a form of hard CC may be used, such as Elise, (Cocoon) or Jinx (Flame Chompers). To really torture the Hero, you can play Fiddlesticks.
No Fair: Add a third Villain, forcing the Hero to contend with three of them. The offside rule must still be followed.
Carry Me Support: Add a second Hero to play support against two Villains. The offside rule does not apply, and the Villains may go wherever they like. It's up to the Heroes, both ADC and support, to keep the Villains at bay while gaining CS for the ADC.
Drill 3: “The Excel Drill”
Hero chooses Elise. Villain chooses any champion with a melee auto attack. Both players take maximum sustain, especially mana regen for the Hero. Play through the first two levels passively. Starting at level 3, Hero must land the following combo on the Villain, all within one second of the first spell cast (Human Q):
- Human Q
- Human W (The spider must hit the Villain for it to count)
- Spider Q
- Auto Attack as spider
- Spider W
- Spider E to safe minion, in the direction of Hero's tower.
Be advised that Elise's human W (spiderling) will jump on whoever she uses her Spider Q on, provided that it hasn't exploded yet. It's advisable to throw the spiderling away from the lane towards nobody, to ensure that it doesn't explode prematurely. Be careful, this is a difficult mouse movement.
Hero attempts this combination whenever the cooldowns are up. Both champions must do their best to CS, and are only allowed to drop one CS per wave. The Hero “wins” if he can land the full combo before 10 minutes pass. Even if the Hero “wins”, continue the drill for the full 10 minutes.
If no one is available to practice, the Hero can play against a bot.
One of the biggest obstacles to improving with a champion you already feel comfortable with is mechanics, and not specifically the act of farming. You need to be able to get the most out of your champion that you can, especially moves that cannot be directly countered. This means entering complex combinations on the mouse and keyboard.
I really struggled to practice these combinations in game. I seemed to never be able to get the keystrokes right. What I ended up doing was firing up my Excel spreadsheet. I marked one cell as “enemy”, one cell as “escape minion”. I then practiced clicking the right cell, spamming the keys in order, as fast as I can. I eventually did it many times in a row, using the cell next to it each time, leaving me with a spreadsheet filled with “qwrqaw”s in one column, and another column filled with “e”. I was quite proud of myself when I finally took Elise into a game and absolutely TROUNCED that poor Renekton who played against me. Good times.
Two Heroes: Both players select Elise, and take turns attempting to land the combo. Once one player tries it (successfully or not), he can say “your turn”, and it's the other player's turn to try and land the combo.
All In: The Hero must also drink a potion and cast ignite during the combo to get credit.
Villain Fights Back: The Villain selects a champion with some sort of melee disable, such as Renekton (stun) or Garen (silence), and attempts to use it to retaliate once Elise goes in. The Villain can now “win” by landing significant damage in retaliation.
But I Don't Own Elise: The Hero may play any complex champion that they like, such as Zed, Jayce, or LeBlanc. Be sure to clearly define what the winning combo is with both players before you attempt it.
Drill 4: “You Play a Fine Edge”
Hero selects LeBlanc, max sustain. Villain selects Lulu, max sustain. Lane in the middle lane against each other for 7 minutes. At level 2, LeBlanc must have Sigil of Silence and Distortion (Q and W). At Level 2, Villain must have Glitterlance and Help, Pix (Q and E). Both players may choose their skills freely afterward. Hero scores one point by landing Leblanc's Q AND proccing the silence with any other skill. Villain scores one point by landing Lulu's E under any circumstances. Both players must endeavor to take at least 5 creeps per wave.
The first World Series of Poker Champion, Johnny Moss, once complained about changes in the tournament in his later years. Originally, the tournament called for seven players to a table in hold'em, but increased that number to nine. Moss wasn't happy about it; he was quoted as saying “with seven, you play a fine edge. Nine-handed, you need the nuts to break the suckers.” He liked the older seven-handed games, where a player had to play big pots without necessarily having good cards.
Some matchups are easy, and some aren't. Eventually, all players will find themselves in a lane where they are going uphill due to a champion that their champion really struggles against. Here, I've chosen LeBlanc, playing Lulu. Lulu's a mean bastard with her ability to land her non-skillshot E, and using it to also land an nearly impossible to miss Q. Leblanc can counter this with a VERY slight edge she has: there's 50 range or advantage on the range of her Q over Lulu's E. If LeBlanc can land these max-range Qs on Lulu without taking any punishment back, she can then get the advantage in the lane by getting the silence, and landing her other abilities. The window is so small though, and it takes a lot of practice to not only cast the spell, but to immediately move LeBlanc to safety the make sure Lulu still can't get her cheap E, and to setup Leblanc's other skills. After all, a LeBlanc Q by itself isn't winning any lanes, so LeBlanc's player must successfully land her other abilities, get the silence, and win a successful trade. Fair warning: this drill is VERY hard for the Hero playing LeBlanc!
The Excel Variation: Merely proccing the Q isn't enough. Leblanc must land both of her other abilities plus an auto attack to score a point. After level 6, she must hit three more abilities and the auto.
All In Excel: Like the Excel Variation, except LeBlanc must also drink a potion, use ignite, and use an item active (DFG) if she has it.
Use Another Matchup: Instead of LeBlanc v Lulu, you can use any champion against any other champion that is a tough matchup. Be sure to examine each champion's abilities, devise a way for the underdog to win the matchup, and award points to players for succeeding or failing. For example, take Singed v. Teemo. Singed scores a point if he gets both a Fling and a Goo to hit Teemo within a second of each other. Teemo scores a point every time he lands auto + Q + auto.