Like every other game to get it started you need to sign up and download the game.
Here is the link to sign up:
While you are waiting for the download.
It’s time to think which play style that might suit you the best, is it AD range, AP mage, AD bruiser/tank or support? I wouldn’t recommend for you to start as jungler right away, as you are level 1 and you don’t have any runes (more on level, mastery and runes later).
Also you don’t have any champions unlock yet, so you need to plan who and what you are going to buy. There’s always 10 free champions rotation for you to try every week. However, it’s better for you to have your regular pick available anytime.
Here are some of the cheapest champion(450 ip) that I recommend. Sivir (AD ranged), Annie (AP mage), Ryze (AP mage) and Soraka (Support). Note: you will gain ip(influence points) by playing normal/ai-game.
More on in-game details next.