To apply a powerup, simply drag it from the powerup list (bottom right, flash-icon), to a unit on the map. Be careful though, there is nothing stopping you from ordering an airstrike on one of your own units.

Once applied, the powerup either takes immediate effect, or it sticks to the unit until activated. In the latter case, a small icon will appear next to the unit when you hold the cursor above it.

Some powerups are activated when the unit is attacked, others when it moves or have other powerups applied.