make sure you spend the time on the prep work...clean the cabinets with a degreaser. Fill in any holes with wood filler. Then sand and prime with a good oil based primer even if you are going to use latex paint. Then paint the first coat and lightly sand before you apply the second coat. This is going to take some time but if you take it one step at the time and don't scrimp on the prep work you should be very pleased with the end result.
If they are painted and not laminated, you need to sand them and wipe them down to make sure that they are indeed clean and free of grease. Prime them especially if you're not sure about the previous paint product. For a really nice finish, oil paint is still the best way to go on kitchen cabinets. It still dries harder than any of the waterborne finishes out there and once it's dry, it's dry and it holds up better. If oil is not an option, use a waterborne like Cabinet Coat. It will need a few weeks to set up 100% so be gentle with the cabinets for the first few weeks - no washing. The label will say it's a paint and primer in one, but we still think a primer first is the way to go.