FIOS will mean CableCard. Basically, you request a cablecard from Verizon, and they're required to give it to you, so that you can get TV channels via your own device. That card then goes into a tuner device, and you have them activate the card+device by calling them up on the phone.
There are two main cablecard devices that work with backend software that is XBMC-friendly:
• Ceton InfiniTV4 PCIe tuner, that goes inside a PC
• HDHomeRun Prime, which is a stand alone network device (and can provide LiveTV even without a backend set up, but a backend will be needed for recording)
With cablecard, some channels are marked "copy once", which means that only certain software can access it. Mainly, software that doesn't work with XBMC, due to DRM restrictions. However, from a quick google, it sounds like FIOS only flags premium channels as "copy once", like HBO, Showtime, etc. I don't know for sure, so you might want to double check before investing any purchases into this endeavor.
The
PVR (wiki) pages should have some backend software marked that works with CableCard. I've had some problems getting TVHeadend working with an HDHomeRun Prime, and I got frustrated as heck trying to get MythTV to work, so I don't really have a strong recommendation.