Drywall or plaster ceilings? Joists 2X6? Conventional frame or trusses? Joist spacing?

If drywall, draw out opening and cut with a utility knife or multi-tool. Cut as much of the joist as possible with a circular saw. Finish with a reciprocating saw. Header off cut ends, frame sides in. Apply trim so that it over hangs openings 3/4” around. Cut a piece of plywood and attach some rigid insulation to the back for a cover.

Don’t hack the opening out with a saws all. Damn bunch of wood butchers.