Looks like a 4 door car? You can remove the inside door panel by first removing the knobs and look for screws inside any cubby holes or hand holds. Then use a pry tool around the edges to loosen the push in snaps.
Now with some scrap wood and the cars jack, you can rig up something that goes between the hump in the center of the car to the door panel with the jack in the middle and use the jack to push the panel in place. You will want a thin piece of wood with a little flexibility that just covers the dented area, 1/2" plywood should work, so that the force is evenly spread over the dented area.
You probably will not get out the worst area of the dent, but I would not worry about it for now, just pop the larger area into place. If you use a hammer, you will leave behind a bunch of pings that will always show.
Once done, paint over with duplicolor spray paint or a matching paint from the dealer. If duplicolor has the matching paint, it will be the cheapest way to go. Duplicolor is a brand of paint found in many auto parts stores.
It will not be perfect, but it wont stand out either, at least not like it does now.
BTW, if you want to prime the bare metal, and that would be a good idea, use an etching primer or a zinc chromate primer instead of automotive grey or red.