It seems like you are going to have a needle localization surgical excision. This is a two step process.
Step One: Needle localization. This is done in the radiology department. The tech will do a "scout" film mammogram of the area with the fibroadenoma. This is just a one view mammogram using a paddel with a square opening and gridmarks. The radiologist will use the gridmarks to figure out where to put the needle in. The radiologist will use a needle with a wire inside and insert it directly through the area with the fibroadenoma. They usually give you some lidocaine, but some don't because they say that the lidocaine hurts just as much as the needle itself. The tech will take another picture with the breast compressed in the perpendicular direction. The radiologist will probably have to adjust once or twice so that the needle tip is 1cm past the lesion. Some needles are designed to be removed with only the wire left inplace. Others with both the needle and wire in place. They'll probably put a styrofoam cup over the contraption and send you off to the OR. This whole thing will probably take 30 min to 1hr. People generally don't like this procedure too much, not because of pain, but because you have to be compressed for a fairly long time 15 to 30 minutes.
Step Two: Surgical excision. This is done in the OR or short procedure room. The anesthesiologist will come talk to you before the procedure. They'll start an IV. They'll take you into the procedure room and they'll give you some general conscious sedation to make you drowsy. You won't be completely out, unless you just fall asleep. The surgeon will prep you and give you more local anesthesia (lidocaine/marcaine etc.) The surgeon will make an incision and use the guide wire/needle to find the fibroadenoma. They may or not send the excised lump for a specimen radiograph. This whole thing will probably take about 30 minutes to 45 min. Most people tolerate this pretty well because they don't feel anything and bleeding is better controlled than with a needle biopsy. The draw back is scarring and disfigurement of your breast, depending on how much breast tissue you're starting out with.
Overall, this is a pretty simple procedure and people do very well with it. You definitely need someone to drive you home since you will be groggy from the sedation. I would also recommend brininging a supportive bra.
Generally speaking, if your core needle biopsy was 100% benign, then this procedure would be completely your choice/optional. Also, the cysts you're going to have removed, that is probably also your choice? You really should weigh the pros and cons of having any or all of them removed, since it is probably optional. I trust you have already weighed the pros and cons and made a good informed decision.
Good luck to you.