There are two shops 

the shop in game and the shop out of game 

The shop in game looks like this

This is where you spend the gold you get to buy different items to help with your gameplay

The shop outside of game looks like this

You can buy champions, skins, icons, exp boost and ip boosts this is where you will spend the ip you get after a match

to buy a champion you need a certain amount of ip

some champions cost 450 ip while others can cost 6300ip

or if you want to get a champion but don't have enough ip you can buy rp(riot points) and buy the champion

Next chapter: Rp and ip