In Resident Evil 6, you can use the skill points you collect from your kills to purchase skills.
You can’t purchase skills while you’re playing though, you have to do it either between missions, or at the start of your game.
When you’re between missions, look for the Skill Settings option.
At the start of your game, you’ll see Skill Settings after you select Play Game -> Campaign.
You only start with one set of three skill slots to choose from at first. Once you beat the game you can unlock more skill slot options that you’ll be able to select from during gameplay.