My provider assigned me a private IP address. Can my router still work with them?

The router will work with a private WAN IP address. The setup will be the same as any other static or dynamic IP address.

If the provider is issuing a 192.168.1.x IP address for the WAN IP, we recommend that you change the LAN IP Address to 192.168.0.1.  To do this please do the following:
Open your browser and input
http://192.168.1.1
You’ll be prompted for a User Name and Password, by default there is no User Name and the Password is admin.
After the Setup page opens, change the LAN IP address from 192.168.1.1 to 192.168.0.1
Setup the WAN Connection type, normally you can just leave it on Obtain an IP Address Automatically unless you have directions from your IPS saying you have a static IP address.)
Shut down all the computers on the LAN.
Unplug the power from the router, and the Cable or DSL modem
Wait for 30 seconds
Power up the Cable/DSL modem and wait for the DSL or Cable LED to go solid.
Power up the Router
Power up your PC’s.