I'm not sure that you can with an entirely successful outcome. The surface is so hard and impenetratable, of course, that it will be difficult to get a good adhesion. If you decide to proceed, I would use an electric sander to attempt to roughen the surface first... Good luck though!
You can buy primers especially formulated to go over formica. which you then paint over. I have found it easier to use a gloss roller to apply the layers of paint rather then a brush to get a more even finish although if you are good with brush work a good quality varnish brush will achieve the bes finish. You can also use an easy sand preperation such as ESP and then apply the finish of your choice.
Finally I have seen some formica which was over painted with tile paint which worked well and seemed to be standing up to wear and tear, although I'm not sure which make/brand it was possibly international.
If you are attempting a large area it may be best if you could do a few sample boards before you start.
Good luck