Welcome to the game, and one of the worst online addictions!
Warding and Oracles, and a really good video at that. It not only states the objective timers (defined in video), but goes into a fair amount of depth for explanations for when and why.
Last Hitting, a very useful skill for most champions that aren't support and some junglers; those champions get the gold/10 items such as Philos Stone, Kage's Pick, and Heart of Gold, as well as use the gold boosters from masteries and, post-20, runes. Same praise as the previous video, but it's the same commentator. Video also includes a brief mention of Zoning, which while mildly important, is merely just keeping your opponent from getting near the minions.
Beginner stuffs, some good basics here. With a number of things that aren't covered on in the tutorial. I'd like to add that you shouldn't buy any runes until level 20, any of the others are quickly outpaced by the higher tiers. If anything, you should save your IP for either champions you
really want, or to buy at least a full rune page at level 20.
Next,
support tutorial. Healing, since this video has been released, has been nerfed a bit, to the point where it's not such a big deal any more. Usually your lane partner will pick up Heal/Flash(Ghost) and you'll be there just to help sustain and win lane. The video doesn't mention all of the support champions, but those ones that have been mentioned have heals. Others that I've seen are Fiddlesticks, Nunu, Leona, and Lulu.
Jungling [part 1], defined in game, with explanation why such a character is good to have in game. The video defines some of the terms mentioned in the warding and support videos. The video also has additional timers on objectives on when they first spawn, with explanations on what happens upon the objective's death. Not a complete video guide, but holds promise for further in-depth explanations.
Also, for some guides:
solomid.net and lolpro.com are both good sites for getting ideas of how to build, use, and improve on how you play a champion. If you wish to theorycraft on champions, go to leaguecraft.com
Oh! And make sure to join in the Gaia Online chatroom on the PvP.net client
And always, have fun!