I did this using models own 'Matt black' as a base and acrylic neon paints to do some nail art. To seal the acrylic paint and make it stand out properly I top coated the design so you can't really see how fab the matt black polish is but it is very matt so I definitely recommend it! The reason I've used it even though I wanted a shiny finish is because the quality of this black is fab, it applies well, dries quickly and is opaque in two coats with no streaks.
The neon paints I used are these ones from HobbyCraft. I also used some makeup wedge sponges which you can get in Poundland, on eBay and from most supermarkets.
I ripped the sponges so there were little dips and wells and rough parts etc and then working one colour at a time I gently dipped the sponge in the paint and sponged it over all the nails. I then left that to dry before moving onto the next colour. When I had done all the colours and all of the paint was completely dry, I top coated and was left with this design!