Powers are your “spells” or activated abilities that can be triggered by pressing the button where it was mapped in the bottom right of your HUD. Most projectile powers tend to home in the target but some powers will require you to manually aim in order to hit the intended target.
Powers can be assigned to different buttons via the Skills screen. There are only three slots for activated powers that you can use at a time and assigning them the left, middle, and right slots will map them to your L1, L1+R1, and R1 buttons respectively.
You can also see which power has an alternate function if you held the button it was assigned to. For example, tapping the button for Overload activates normal the skill normally. If you press and hold the button before releasing it, your Overload will get charged which will make it chain to two additional targets. Another example is the Omni Grenade; tapping the button once will throw the grenade while holding the button will “cook” the grenade which shortens the fuse time, making it explode faster after throwing it. (Be careful since it can explode on your hand if held too long)
Most powers just need to recharge before you can use them again. You can see the remaining recharge time in the lower right corner of your HUD as the power icon slowly "empties". When the power background is transparent, then the power can be used again. You have to keep an eye on this from time to time during battle to ensure that you have the skills ready for Power Combos or other tactics you may have in mind.
Recharge speed is affected by your character’s carry weight limit. Carrying heavy Weapons or multiple smaller weapons will drastically reduce your recharge speed, even with the recharge boosts from specific Profiles active. Combat Fitness for example can increase the weight capacity when ranked up, allowing you to retain your normal recharge speed while also carrying your preferred loadout.
Some Powers like Omni Grenade or Trip Mine have no recharge time but they use consumable “ammo” called power cells. They can be recharged from Forward Stations or picked up from ammo crates.