To start, apply your base coat and base colour. I used one coat of Barry M Mint Green. It doesn't matter if the polish is opaque or sheer, most of it will be covered with other polish.
Next, apply random blobs of different coloured nail polish over most of your nail. I used Nails Inc Hanover Street, OPI Give Me The Moon and w7 Green Dazzle. You don't want the blobs to be too thin so they won't spread slightly across the nail, but you don't want them to be too big so it'll cover your entire nail.
Then, I used the smallest end of a dotting tool to move the polish about a bit, mixing the blobs together in a swirly motion. Don't mix them too much though or you'll just end up with one colour. If you find you've got too much of one colour, add a small drop of a different colour and mix it in slightly. It doesn't matter if your nails aren't uniform, each nail is meant to be a bit different.
When you're happy with your nails, add a top coat and you're done!