You buy RP (Riot Points) for real money, then buy the skins you want. It's how the game stays alive with being F2P.
Though you can get lucky and get some nice skins in the caches you get (You get a cache by performing well and getting an S- rank or higher), though you need a key to unlock them, and those just gets rewarded to you randomly as you play (usually if you are a honorable player etc).
I was SUPER lucky with some of the caches, and have gotten Elementalist Lux (Legendary skin).