Speedy,
I painted my units almost 2 years ago with Ronseal "Tile" paint. Dont laugh! I'm pretty sure it's the same as the Kitcken units paint that they sell. Both paints are available in a range of colours. Check out the Kitchen units paints first. Easy to find on any good DIY store.
Like Ninsaga adviced above, make sure the units are well cleaned, using soap or washing-up liquid and warm water, or better still, sugar soap. Cupboards near the cooker and extractor hood can be quite greasy.
Give them a light sanding with fine sandpaper or some steel wool. Then give them a dusting to remove any fine dust or metal particles if you were using steel wool. Don't use a Brillo Pad, it leaves too much fine metal particles behind.
I took off the doors and painted them on top of my kitchen table though it's possible to paint them without taking them off. The general advice seems to take them off and paint them. It worked well for me. Taking off the handles makes things easier too, just replace them when the paint is well dried.
Be careful to put on an even layer of paint, as thick patches and heavy brush strokes show up very easily when the light is shining on them.
I found one coat to me enough
good luck with your painting!