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You would tape something that large with drywall tape, and get some premixed drywall mud and put it on there smoothly. Once dry, light sand, and do coat 2. Same as before, and then put on coat 3. Primer it and paint it when you have it nice and smooth.

Drywall tape is for taping seams. Cut out the drywall in the damaged area in a square/rectangle. Make sure you cut out all the damage area. Replace with new drywall and then tape, mud and sand the seams.

Could I fill that in with spackle and let it dry?

I’d use joint compound (mud), and build it up slowly... apply a thin layer, let it fully dry, then apply another thin layer and let it dry... repeat until it’s filled and smooth. Layering it on thinly like that will keep it from cracking.

Cut out the drywall in the damaged area

But it isn't drywall, it's plaster.

I should of said plaster. You still need to cut out the damaged area and from the look of the picture it isn't a small area. It looks like the plaster is failing and not attached to the lathe anymore.

So compound wouldn't be a good idea? I'm trying to find the quickest and easiest fix.

You can still use drywall mud on plaster. It is going to be hard to get a level surface if you just use mud without patching with drywall. If you are just going to try to cover up the damaged area I would at least use Durabond 90.