Create a League of Legends Account

This article will give you a direct overview on creating a League of Legends account.

Steps

Open a browser window
Copy or click on the link here.
Enter a desired username, password, and an email address for confirmation.
Download and install the game client form in the link following account creation.
Once installed, open and log in with username and password.
Follow the instructions to choose your summoner name and picture.
Click 'Play' button at top of screen to begin a game.

Your Summoner Name is different from your Username. The summoner name is the one you use to log in to LoL once you download it, whereas your username is the one that is viewed in the game and seen by all when you play.