Where can I find a League of Legends tutorial?
The best place to learn everything about League of Legends is its very own Website.
Another great source to learn even more, however best visited after you've learned at least a bit of the basics, is the Wiki.
As @nimcap mentioned a great way to practice is against easy difficulty bots in custom games that you can make from the in-game menu. There are also tips and hints EVERYWHERE that help new players become introduced to the game. One example is if you look on your CHAMPIONS page in your in-game menu you will see some Champions are listed as recommended. These Champions have been specially designed to be easy to learn and use, just for newcomers like yourself!
You might also have noticed that each hero has a recommended item loadout displayed when you open up the in-game shop during a match, to help players such as yourself with quick and easy item recommendations until you get the hang of things enough to make your own educated choices.
Your question specified a Tutorial and the best ones can be found in these places.
The First is in-game. There is a built in tutorial the game itself offers you right with all the other game modes accessed through the PLAY button.
Another good place to look was already mentioned by @nimcap, the Mobafire website. See his answer for the link.
The League of Legends website was already mentioned at the start of my answer, but I'm going to mention it again here with special focus on their Forums. There is all kinds of posts there to help new players, including but not limited to an entire section of their forums specifically devoted to tutorials for new players. Any stickied post should be sufficiently detailed enough to help you with just about any question you could ask.
I'll close with a generic peice of advice. League of Legends (and respectivly DOTA or any other M.O.B.A.) tends to be EXTREMELY difficult for new players. It's obviously not the same for everyone, but for most the learning curve is very steep. This is further aggravated by the fact that the player base (the people you end up gaming with in your average random game) tend to be very unfriendly to new players, because they do not want to loose and see you as a hinderment for their team.
Do not be discouraged, do your best to ignore the flaming that will inevitably occur, and simply learn from your mistakes and try again. Good Luck!
LoL offers playing against bots option. If you know the basics, you can select the easy mode against bots, and practice your skills.
There are also guides on how to play specific champions, one such place you can find lots of guides is Mobafire.
If you're looking for an awesome set of video tutorials that should see you through to level 30, I would highly recommend looking at Optimus Tom's series In The Zone.
He does a great job of walking you through the basics of LoL and explaining how to play champs and roles in a very in-depth manner. He uses a lot of tips and guides from the pros, and it should definitely help you on your path.
Good luck and see you on the Fields of Justice!