I refinished this one last summer, but the top was veneer with some water damage and there wasn't really much I could do, so I just sanded what I could with a palm sander. The final touch was going to be a urethane resin to coat the graphic and smooth out the bumps but I haven't gotten to that yet.
You can see the pressboard poking through the veneer where it was bubbled:
I'd imagine some wood putty on the gouges/chips like Guy said and then some sanding and primer would be a good base, then paint and then a urethane resin finish to coat the top and smooth it all out.
I used some JB Weld KwickWood for a few places on mine. Worked out great.
Not sure what you mean by swollen though. Swollen as in warped?