Frst, a word of CAUTION; DO NOTdrill from the bottom up, it can cause splinters that the register flange may not cover.
Pencil the size required on the finished floor(from above)
then, from above only, drill 2 holes kitty- corner to each other, keeping the edge of the holes within the line.(the size of the hole will depend on whether you are going to use a small key hole saw to start the cut or if using a "jig" saw) Usually a 3/8" hole will do. A "jig saw" with a 1/4" coarse blade will do a good job on supply registers such as 4x10 or 6x10 openings.
If the openings are for larger (return air) then a circular saw could be used being careful to not overcut the line.
Also, if using one of these power tools, it is a good idea to use masking tape to protect the floor from getting marred from the tool's base plate.
Good luck.