Your first two or three BOs will be automatically added to your crew as you receive them. As you progress through the game, you can receive additional BO's through either mission rewards, "purchasing" them with Starfleet merits (which you earn completeing missions), or from time to time a new BO will request to transfer to your ship (mission: New Bridge Officer).
To equip them, just have the stuff in your inventory, and then press U. Select them, and drag and drop their new equipment into the slots. BO's can only equip 1 weapon, 1 body item, and 4 consumable items. They cannot equip kits (as they are, in a manner of speaking, a kit unto themselves).
On things you gain skill points for, you also receive Bridge Officer points. You upgrade your BO skllls using these points like you do your character. You can also promote them by spending Starfleet merits after you have spent a certain number of BO points on them. (To promote one to Lieutenant, you need to have spent 200 BO points on them and it costs 300 Starfleet merits.) A couple of cautions about promoting Bridge Officers:
1. They can never be promoted to a rank equal or higher than your current rank, and then can't (I believe) be promoted higher than Commander.
2. While a BO can be promoted at any time, their space skills will be limited to the level of the Bridge Officer station their assigned to. In the Tier 2 ships (Lt Cmdr), this means that with the 4 stations, all of them will have access to their Ensign space skills, but only one of them (the same class as your ship class) will have access to their Lieutenant space skill. On the ground, they will have access to all their ground skills they're able to use.