Determine the new vent's placement. Place floor vents between floor joists. Place ceiling vents between ceiling joists. This gives you support for the frame.
Mark the dimensions of your register with a pencil. For floor, use the circular saw to cut the hole. For ceiling, a drywall saw is adequate. Remove any little burrs or imperfections.
Measure the inside of the gap and cut two sections of 2 by 4 to these lengths. Generally these are anywhere from 12 to 16 inches between joists.
Place both of these pieces between the joists and secure with nails. They need to be right on the edges of the holes you cut.
Measure the length of the other gap that has not been framed in. If the hole is the same size as the space of the joint, no further support cuts are needed. If it's not long enough, make the two new cuts on the 2 by 4 to length.
Place the two new pieces into the frame. These will butt up against the two new pieces you have installed. Nail them in to place. The frame is now ready to have the vent added and the hardware for the room.