It's a little bit tricky to master, and quite messy but totally worth it!
You will need:
Cocktail stick or similar
Different polishes (2-5)
First things first make sure you tape up round the edges of your nails. This will help to reduce cleaning up time later on.
Then fill a regular bowl with room temperature water. The size of the bowl will actually make a difference here- if you have a really small one the polish doesn't have room to spread out so is too thick, if you use a big one then it will be less concentrated and will have a more transparent effect- which is ok actually if that's the look you're going for.
Most people recommend you paint you nails white before you start.
If you're using a normal cereal/pudding/eating bowl then I actually haven't found this to be completely necessary, although it will depend on the colours you're using.
For argument's sake just go ahead and paint your nails white, or even a base colour that matches the colours you'll be marbling with.
Now comes the fun part!
Open all of your polishes and line them up in the order you want to mix them. You have to be quite quick with this so it really helps to have them ready.
Once your nails have dried add a drop of your first polish in the middle of the bowl. It should rest on the surface of the water and dissipate- spreading out across the surface.
Drop your next polish in the middle of that polish, your third in the middle of that etc and keep layering them until you feel happy. Use each colour at least twice. I usually do not use more than 5 colours- I tried to do a rainbow but
a) your nail is not big enough to fit all of the colours on anyway
b) by the time you've added each colour twice it starts drying out and doesn't stick properly.
Grab your cocktail stick (or equivalent- I started out with a pen!) and draw lines across the polish in the water to swirl it together a bit. When you're happy with your pattern simply rest your nail in the polish on the surface of the water and blow on your nail. This part is important!
Keep it there for 10-20 seconds (this time will vary with different polishes etc so it will be trial and error, but you'll figure it out!)
Remove your nail and it should be marbled!
Twirl your cocktail stick in the polish and it should all gather up in a little ball. Take it out of the water ready for your next nail!
If you get really good you can try doing a couple of nails at once to save time, but once you get the hang of it it really doesn't take as long as you think.
Once you're done just seal them with a top coat like regular polish and remove the tape. If it still managed to get past the tape then clean it up with a cotton bud and some polish remover.
I spent about 2 hours doing it the first time I tried water marbling. I tried to go for a peacock colour scheme: