THere are plenty of books and WEB sites that talk about how to repair drywall. Search the WEB using how to repair drywall as you keywords. Or, visit the library or Home Center for DIY books. Perhaps there are 'handouts' that are for FREE.
In any event, you want to 'cut out' the damaged drywall from stud to stud. You need to know the thickness of the joist, then divide that in half. In other words, you DON'T cut out the 'bad' drywall completely across the joist. If you do, then the GOOD piece of drywall (that's still on the ceiling) will have nothing to 'grab' onto, and may sag. Because, after you cut out the bad piece (half way across the thickness of the joist), you'll need to put Drywall Screws in on the piece that's still up on the ceiling (to prevent it from sagging.) So if the joist is 2-1/2" thick, you only want to cut the bad piece out 3/4". This way, the new piece AND the good piece still on the ceiling can be screwed back to the joist. (I hope this makes sense.)
After this, learn how and where to cut the replacement piece of drywall. Screw it up. Read about spackeling and sanding too. THen, I suggest 2 coats of Primer/Sealer, and 2 coats of top-coat paint. Since it's a bathroom, use something like Latex-based Kilz Primer/Sealer along with a GOOD, quality finish paint with a Mildewcide in it (from a Paint Stoor like Benjamine Moore or Finneran & Haley or the like.) Paint Store listings are found in the YELLOW PAGES under PAINT - RETAIL.
My best to ya and hope this helps.
Jay J -Moderator
PS: The bad news it you need to 'cut' out the damaged drywall IF the crack is all the way through. You MAY be able to just screw it back up in place but I can't tell from here if it will be 'level'. TO boot, you may not have a joist to screw it to in order to hole it in place.