I've just completed a successful respray of my calipers so I can help you there. Nothing wrong with what Mori Man has said but you might want another option.........
First you need to wipe off all the crud with a rag. Then rub down all the painted surfaces with medium wet and dry (used dry, you don't want a film of oil rubbing into everything

) Majke sure you get into all the nooks and crannies. You are not looking to get everything down to bare metal, although you will need to completely remove any unsound paint and get corroded alloy down to fresh, shiny stuff - what you are doing is providing a good keying surface for the new paint. So providing to seriously scratch any sound paint that's fine, leave it.
Now you want to get a nail-brush and scrub everything with a soap and hot water, rinse off with clean water and thoroughly dry.
You need to mask off with decorating masking tape all the surfaces you are not going to paint - so that's the inside surfaces. Make sure you cover the pistons / seals. If you get paint on the seals the solvent will bugger them. Now bung bits of bog roll in all the threaded holes - doesn't matter about the others - as you don't want the threads bunged with paint and you dont want paint getting inside the pots. Cover the smooth sealing surface of the hole where the banjo goes in with a circle of masking.
Now you're ready to paint. I placed mine on plastic plant pots, as I could turn them round and get to all parts. My calipers were spilt into halves, which makes things lots easier. If yours aren't split you're probably going to need to suspecn them by a bit of wire and have them hang while you spray.
I used Hycote gloss black engine enamel, which you should get from car spares shops. Needs no priming, gives a lovely finish and will stand the temperature the calipers will get to in use. I gave three coats. Apply lightly and keep the can a foot or so away. Several light coats built up with about 20 mins between is what you want. If you try to put thick coats on you'll get runs, sags, and it will look toad. You need a nice room temperature where you spray, if it's too cold the paint won't go on right and you won't get a nice finish. So you want a heated garage / shed or somewhere in the house. But if you do it in the house you need to dustsheet everywhere in that room - don't underestimate how far the atoms of spray will travel
After you've done, leave for 24 hours for the paint to cure in a warm room, then remove your masking etc. Don't leave it too long as the masking will tend to stick firmer over time. When removing be careful to go round the edge of any oversprayed masking first with a Stanley or you will end up ripping off the edge of your painted surface, leaving a tatty line.
You should get a good, durable finish. Good prep is the secret to good, durable painting. Take your time. If you put coats on too thin and have to do more that's no problem at all. But if you try and put thick coats on and get runs you've buggered it, so err on the side of safety. It's not a hard job, good luck and show us the results!
