In order to check all available boosters, you need to press a special inventory button at the top-right of your hangar view:
Then in an opened Inventory window choose the Boosters tab
Please, note that boosters(except those, purchased in the Store) have an expiration period, after which all non-activated boosters disappear:
In order to activate a booster, hover your cursor over it and press the Activate button under it. Alternatively, you can choose a booster with a mouse click on it and then press the Activate button at the bottom-right of the window:
All activated boosters are limited in time(1) and in a number of battles(2) you can use your boosters in: