There are a number of useful website to help you understand the game more and really help you out
http://eune.leagueoflegends.com/board/ This is the official forums for LoL, this is my first stop most days to see what everyone is up to and talking about, the community. If I find some really good posts i will try to put them here.
http://www.lolking.net/ This is a database updated every week of the stats of games played, You can see which heroes are the most popular, check your favorite players ranks and recent games its like the In-Game summoner profiles that you view but better :p
http://leagueoflegends.wikia.com/wiki/League_of_Legends_Wiki This is the Wiki for LoL, this site is pretty good for looking at peoples blogs on heroes, reading the Lore, finding out Patch notes etc.
http://www.mobafire.com/league-of-legends/browse This site is the best, I still use it today, i remember when i first started playing, I was a big Garen fan after playing Swiftblade/Junero from Hon/Dota I was building him completely wrong, followed a build from this site and instantly saw improvement :D
http://www.solomid.net is a site I have been on more recently, I am a TSM fan and enjoy watching Dyrus and TheOddOne's streams. You can also see featured streamers on the same site like, SKOcelot, Guardsman Bob and the other favorites
The main things i have found out playing LoL are to play it for fun, if you start to get mad because the other team is laughing at your, just ignore it. If you have a bad player on you team try and lead him through the game. I have seen and been apart of so many games when we are about to lose and turn it around, its never over until its over ;)