Power ups work the same as other buffs. Put the icon in your toolbar, click, and they last for half an hour. In addition to weapon PuPs, you can also use clothing and armor, so basically three extra buffs. PuPs come in a wide variety, anything from basic stats to profession specific specials, damage increase or chance or action reduction, whatever is right for you. (The Junk Yard lists the different options available.)
Different traders needed to make these:
Domestics = clothing
Engineer = Weapon
Armorsmith = Armor
The higher the luck and reverse engineering skill of the crafter, the better the PuP.