The basics are:
- You will have to make sure your router can do VLAN routing (which most modern routers should).
- Create two subnets on your router (you already have one so create one more). The second one needs to be assigned a VLAN number (e.g. VLAN 10). It will need a different subnet than the one you use now. So if you currently use 192.168.1.0 than the newly created subnet for VLAN 10 could be on 192.168.2.0. This will be your newly tagged VLAN subnet. Your first subnet you have been using is probably untagged (or it defaults to VLAN 1 on some routers)
- On the new switch, you will need to set the switch ports you desire to be in this VLAN to VLAN 10. These are generally referred to as tagged ports. The ports you don't want tagged (e.g. the subnet you use now) can be left untagged (also called access ports).
- The uplink port on the switch back to the router needs to be set as a "trunk" so it will carry tagged and untagged vlan traffic.
- The port on the router may/will also need to be set to trunk.
That is the gist of it. Setup and terminology can vary but that are the basic steps.
After everything is working and you can route (connect) to things in VLAN 10 from your untagged VLAN then it's time to create some firewall rules that blocks all outbound traffic from VLAN 10 to the WAN.