They should run Fiber-Optic to an interface box.. From there out you either run CAT 5 or 6 (i'd run 6) or Wi-Fi... Same as you are running now.
The only things that will need to be redone and you may be able to get them to set it up so you don't have to do that.
You may need to scan for Wi-Fi access points and select your new one and enter a new SSID.
You may find your IP-addresses have changed.
Now for Television.. (if they stream both TV and Internet over the fiber) I'm not sure how that works. if they convert to NTSC or QAM and feed your house with RF from a micro transmitter in the box or if they put fiber to HDMI set top boxes on every TV in which case fiber lines will need to be run.
I simply do not know.