Modifying a weapon requires mods (purchased or found). Once you have mods that fit a specific weapon type you own, you may go to a Weapon Bench and apply it. To do so, select a weapon and you should see the bottom right part of the screen that says "Weapon Mods." Press which brings you to another screen. Select the mod using then press to confirm. The first time this can be done is in the Citadel in the Embassies (shooting range), but there is one in the Normandy when you finally get aboard as well.