A good way to understand the game a bit better would be to watch pro players on streams or with the upcoming LCS watching a few live games. The LCS is a huge tournament that is world wide and has all of the best teams competing. You can watch pro players solo que (playing by themselves) or watch replays of LSC or IPL tournaments on Youtube. A good place to find streams of good players is on http://www.solomid.net/streams.php. They feature streams of pro players who stream their live games. On their streams you can comment on the video while it is live and more than likely others will be watching too who would be more than welcome to answer any questions that you might have about the stream. I personally think that watching pro player solo que is better for personal improvement. This is because the solo que streamers will be more focused on one Champion as apposed to multiple Champions where it can be hard to understand what the individual Champions are doing throughout the game. This being said, watching a team play is not bad because it gives a better understanding as to what to do in terms of being a team and playing like one. Other good places to watch streams or old videos would be:
http://www.twitch.tv/directory/game/League%20of%20Legends
http://www.mobafire.com/league-of-legends/videos
http://www.solomid.net/videos.php
I hope this helps improve your game.
League of Legends: Champion Select 