Not entirely sure this is the right section....but
Same way you'd paint any other body panel.
Best done with a professional booth/gun/paint etc.
But, since the spoiler is not a large panel, you could get away with rattle-cans as long as everything is super clean, and you do it right.
Wash the hell out of it, use a wax remover, and let it dry.
Sand it down with some 320-400grit, and wash it again, let it dry.
Lay down some primer to give it a good base for the paint to hang on to. 2-3coats
Sand the primer down with some 400, and make sure that everything is nice and smooth.
Spray your paint on. Do a tack coat first, followed by very light, even coats. 2-3coats
Spray the paint in a medium 'wet' coat. As it goes on, it should look like a nice even 'glassy' coat
Let it dry for atleast 24 hours, the longer the better.
Sand it with 1000grit, and spray on your clear coat. 2-3 coats, more if they are light coats.
Let that dry for a few days, and polish it with some compound, and wax.
Sounds like alot, but it isnt really, since the spoiler isnt that large of an object to be painting.