Exercise. You can do that even outside of real games in simple custom bot games.
I can suggest:
*cs training. Set yourself goals like 100 cs at 10 mins, 200 at 20 mins etc. and try to increase it with every game. If you want to get serious, try not to miss a single
minion on your lane. Use your skills, summoner spells and items to achieve it if necessary.
*Get familiar with your desired champ. First, read through his skills and get some information about him from http://de.leagueoflegends.wikia.com/wiki/League_of_Legends_Wiki
Next, think about which stats/stat-combinations your champ will benefit from the most. This will help you to decide how to build your champ and which items could potentially be useful in your builds.
Also get familiar with your champs skill order. This is a biggie. If you mess up the skill order it can leave you handicapped as badly as if you mess up your build. The important thing about skill order is to
1. Look how much stats a skill gives at lvl1
2. Look how much increase a skill gains for each lvlup
Congrats you can now decide for yourself in which order to build without looking at a guide.
Also experiment around with masteries, runes and spells or look up some non-mobafire guides.
*mechanical training. Exercise how to clear jungle camps faster, learn the respawn and spawn timers, use the hotkey functions in-game to use items(1,2,3,4,5,6) learn your skills via hotkeys instead of having to slowly moving your mouse down to skill one point into W cause you just lvluped during a fight and need that W to win while your enemy ults you for 1k damage before you skilled your W and you're dead.
Use smartcast depending on which champ you play. If you are Pantheon and your enemy is pantheon and you both are low health, the one who finishes the other pantheon off is the one who smartcasted his E. If you use smartcast on certain other champs however, you are just handicapping yourself...
Enable timestamps in-game. If you want to learn the spawn/respawn timers the only way to keep track of them is to use your timestamps properly. They are so easy to use once you enabled them.
Just killed Dragon? Write dragon or w/e into your chat. It will show:
20:33 - Flevalt: Dragon.
Dragon respawns in 6 minutes so now count up and write it again into chat so your team knows it too!!!
26:33 - Flevalt: Dragon at 2633
Now ward it the minute before it respawns. Congrats, you have just auto-won your next dragon fight.
*And lastly just keep playing more games. There is a lot of knowledge about synergy between champs, counter between champs and certain effects of items/skills on other champs skills/items that you'll only learn by experience. So just keep playing or do some 1v1 test-runs with a friend to see what happens e.g. when a blitzcrank hook grabs Ezreal while he uses E or what happens when a silence hits Rumble while he overheats, if Rylais slow effects Fiddles drain etc. etc.