I am not sure about what I am asking.
Before I make any changes I just want to make sure it doesn't impact everybody at home.
If your router does not support setting the DNS server, you can use Pi-hole's built-in DHCP server; just be sure to disable DHCP on your router first (if it has that feature available).
I can't find the dns options in my router (BT Hub)
If I enable the DHCP server - how will the client on the LAN be assigned an IP address?
Look for the DHCP settings in the BT Hub. They might be in a section such as LAN or Network.
There are user guides for the different models here which may be useful.
You need to turn off the DHCP option in the Hub. Make a note of the address range it uses before you do. Then you need to turn on the DHCP option in Pi-hole. You can use the same address range. Enter your Hub's IP as the gateway address.
Once that is all done, disconnect and reconnect all your devices from the network so they find the new settings. Perhaps the simplest way to do that is to reboot the Hub so they are all forced to reconnect. If they are using the Pi-hole DHCP you will see them on the Pi-hole DHCP page under "Currently active DHCP leases" when you refresh the page.
If Pi-hole is to become your DHCP server, you'd also have to configure the machine hosting your Pi-hole for a static IP address before you disable your router's DHCP server.
It would depend on that machine's OS release how to achieve this.