Filling holes in floor where heating ducts used to be?
Filling the holes is the easy part. You put a scrap of 2x4 under the floor across the hole on each side and run screws through the existing subfloor to fix the scrap in place. Then just fit a piece of sub floor in the opening and screw it onto the 2x4's.

The hard part is replacing the flooring itself. If it's hardwood, you have to try to match the grain and probably remove a few pieces so there isn't an odd rectangle in the grain. If it's carpet, you need to get a scrap of carpet (hopefully one was left from the last install), align the grain of the patch with the existing carpet, and fix the scrap of carpet in place with glue strips that are heated with a special iron to melt the glue. A professional carpet installer can make this spot disappear in a way most DIYers can't.

Since you have a temporary solution in place with the vents that are there, I'd suggest holding off on removing them until you decide to replace the flooring if that's at all convenient.