Assuming your flights were booked as a single itinerary, you will not need to go back through security nor pick up any checked luggage in Denver. When your first flight lands:
Get off the plane, taking your carry-on luggage with you (note 1)
Look for a monitor displaying departing flights
Find your second flight and note its gate number
Go to that gate and wait until it is time to board. (note 2)
You should be given boarding passes for both flights when you check in in PDX (or online). If something happens and you lose your second boarding pass, it can be reprinted at the departure gate of your DEN-BNA flight.
If your flights were not booked as a single itinerary, things get more complicated, but I won't go into that unless you confirm it's the case.
Note 1: If your PDX-DEN flight was on a smaller regional aircraft, some of your carry-on luggage may have been "valet checked" or "gate checked" at the departure gate in Portland. If so, you need to pick it up in the jetway as you exit the plane in Denver, and take it with you to your next flight.
Note 2: DEN has three gate areas, A, B and C; every gate number includes the area letter (e.g. A31, B17). Most likely your DEN-BNA flight will depart from the same gate area where the PDX-DEN flight arrived, in which case you only need to walk east or west along the concourse in the appropriate direction until you find the gate. If you should need to go to a different gate area, they are connected by an underground train, which can be reached by going to the center of the concourse and taking an escalator or elevator down.