Testing of the paint type of the old coat is necessary to ensure the paint you are about to apply will bond properly. It is crucial to know what type of paint you need to apply as your over coat.
The simplest and cheapest way to find out is using methylated spirits to test it. You need only gently rub methylated spirits on the surface and if the coating dissolves or becomes soft then the surface is an acrylic paint, and can be over coated with any acrylic coating.
If the surface shows no affect when you rub it with methylated spirits, it is probably going to be enamel paint, therefore you will need to lightly sand the surface with a medium to fine sand paper (120 grit) then use a coat of oil based undercoat, then over coat with either acrylic or oil based top coats.
If you are painting doors, windows, frames or any surfaces that take a lot of wear, use oil based top coats as they are far more durable.