I bought a used one, so I can't say for sure what a new router would mean. Generally when changing the security protocol it's a two step process:
1. On the router, you have to configure the new protocol (wpa2 in this case). Generally this means means setting the new protocol and giving a new connection password.
2. For each computer/device that attaches to the network, you have to find and connect to the new wireless network that you created in step one. This will require you to enter the new connection password.
If you have a lot of computers/devices to attach to the network, step 2 is a bit of a pain. But everything is pretty straightforward. When I upgraded, I had 3 laptops and a printer to add to the network. It only took 15 minutes to add them. Later I bought a PS3. It was trivial to add to the network. So you can do this.