Should I paint Styrofoam ceiling tiles before or after installation?

You can do it before or after installation and each method has its pros and cons. If you choose to paint your tiles before installation, keep in mind that you will need a fairly large area for your tiles to dry for at least couple of hours. Also, if you are painting your tiles before installing them and the color is blue for example, unless your caulk is tinted to that specific color you will have to paint the caulk with a brush to match, after the tiles are up and the caulking is dry ( this process is not really hard at all, just make sure to mix the paint with little bit of water/ Floetrol so that it lays nicely and does not dry too quick and leaves brush marks). If you are painting the tiles after, make sure to caulk the seams and let the caulk dry for couple of hours at least.