What is the best way to patch a hole in the ceiling?

You did not mention what kind of ceiling material we are patching. Here is an instruction from Lowe's on repairing drywall:

https://www.lowes.com/projects/repair-and-maintain/patch-and-repair-drywall/project

Why is the plumber not fixing (or paying) to have fixed for you? See if this helps.

http://homeguides.sfgate.com/patch-hole-ceiling-37698.html

Get that plumber back to fix what he damaged!

When I had to have a faucet replaced in my bathtub, there was no access to the wall in my bedroom. The plumber cut a 15" square hole for access. When finished, he popped in a PVC plate! It can be painted. I just left it white since it is on a wall covered by my dresser.

GOOGLE "pop in cover plates for plumbing access" and you will see they are available. I saw them at 14" but mine is 15"...so I guess they come in different sizes.

Your plumber should have put in a plate for you.

Call another plumber and see if they have one. Measure the hole...you may have to cut it slightly larger. Get a plate before you cut hole larger! You will need for it to be snug so it will hold in place.

You can repair but I would leave access!

Here on Hometalk is some clues on repairing drywall ceilings. Click on links below.

https://www.hometalk.com/diy/repair/drywall/diy-drywall-repair-3011798

https://www.hometalk.com/search/posts?filter=Drywall

hopefully You are dealing with drywall....cut a piece of drywall to insert into the hole snuggly. Tape around the edges with mesh drywall tape and using a putty knife, scrape drywall compound over the edges, allow to dry, repeat the compound if necessary, sand smooth and paint

if you see 2 beams make sure the hole is big enough that 2 are exposed. cut a piece of sheetrock the size of the hole, screw in with 4 or more sheet rock screws, plaster, sand, paint......