I have done two, gently mark out for the trap (use a soft pencil). By using a stud locator, find out where the joists are, or failing that tapping the ceiling should give you a clue. Now centrally within you initial markings, make a large hole with a hand saw. Now you can probe about and find out the exact positions of the joists, its worth amending your hole size and shape so it is up against the inside edges of two joists. make the hole larger, but leave it 3" short of the unsupported section between the joists Now get a batten and clamp it to the top of the not-to-be-cut joists and across the unsupported bits and cut the excess off . It would be a good idea to support the soon-to-be-loose joists. If they are short then a bit of 4" X 2", which overlaps two uncut joists could be screwed in from the top using some decent size screws, or as I do, go back 4" and through bolt a bit of 8" X 4" with 3' overlap each end. I just drilled the holes through the ceiling and joist and gently raked out the plaster so the bolthead can press directly on the laths, the bolts then go through the trimmer. In retrospect, it was OTT, but it did not move or ceiling crack for at least 31 years.
Now you can cut the unwanted joists out. This is a right pain that is sawing off the joist(s) that are running across your hole, it would be good if the cut is vertical, if its problematic, taper the top away from the hole.
Now frame out the hole, use 6" X 1" PAR, tack it on with panel pins to start off with, its lower edge needs to be as tight as possible to the plaster and the box not twisted. N.B. you will need blocks screwed to the inside of the last continous joists to carry the ends of the cross pieces. Pack out to make sure that the box has vertical sides. Fix it on well as you will be resting ladders on it. Now trim the underside with a architrave picture frame, this will hold the loose plaster in place. Line the inside again with some stop beading and make a loft hatch, 18mm chipboard will work, glue 4" of foam to its top. For a "panelled" look, glue and pin on some flat wood on to the hatch.
Job done except for painting.
Frank