You know the champion is using the item when it does something.
For example, when you activate
then your champion will jump forward and bolts will shoot out in a cone.
If you use the active on
then your champion's health bar gets a gray area and they'll get a shield.
All you really need to do is press the button the item is on. Like if it's in slot 2 and you have
, press 2 on your keyboard and your champion will automatically do the action and then it'll go gray for the cooldown. Keep in mind not every item in the game has an active, read the description of it in the shop in-game or on the boards where you see the icons before making a post.