Play bots a lot until you can beat them. If you can't beat bots, I really doubt you will have ANY chance of beating players who know what they are doing. Bots have tendencies that you should be able to pick on eventually, allowing you a window to kill them or push them out of lane.
Play ALL of the free to play champions. If you really want to get good at this game, learning what EVERY champion can do will be to your benefit. Nothing beats you harder then the unknown, so learning what each champion can do is a great way towards preventing that. Also doing this will allow you to find champions you like and will help you with future champion purchases. Even if you don't like the champion, you will learn their abilities and learn what they can do.
Another thing related to playing all the champions, try to find ones that you like and just play them. Try to find a few that you really like and focus on those. Becoming familiar with them will make playing against different champions a lot easier since you have more specialized experience.
This one isn't related to learning the game, but once you hit 20, you will want to buy tier 3 runes. These are pretty expensive, full pages costing up to or even MORE then a 6300 champion. I say at first you should go for more generic runes that can be used on all your champions pretty well such as flat armor seals and mr glyphs. Saving after you are able to find champions you like, will make you feel much better for planning ahead now and reaping the rewards when you are 20, then hitting 20 and being sad you can't fill out your rune slots because you didn't save up your IP.
As a remark to your last sentence, I think you should try to get out of your Tryndamere love phase. Once you do, you will be able to grow as a player :D.
