With a fibre installation the engineer will fit a new box (a ONT - your new modem) This will replace your old phone box and will need a plug socket. The ONT will then connect to your router via a CAT cable. If you continue to use your existing router then there will be no issues.
If you have to replace your existing router you will either need to 1) re-enter all your WiFi settings/passwords on all your wireless devices with the new router's values 2) OR - my preference - change the SSID & password to match the ones on your old router which means no need to enter new passwords etc on your device. (If you don't know what a SSID is option one is easiest!) Wired devices will be fine.
(I've had 3 different ISPs in the last 7 years and in each case I just used my existing router changing the SSID to the previous one and left the supplied router on the shelf ready to send back if/when I change my ISP. As a result my house's wifi SSID is still the one from a BT router 8 years back.)
Your telephone - if you use one - will now plug into the back of the router for landline services.
