First print off your house crests and cut out (I literally googled 'Harry Potter crests' and came up with the one you see here. I just resized them on a word doc until they were nail size). Line them up in the order you want.
Paint your nails with a base coat. I used this metallic blue because it's really hard wearing and I was dressing as a Ravenclaw, but you can use any colour.
While your base coat is still tacky, dip your printed off crest in the water (quickly - don't submerge for too long or the ink will run). Then put it in place on your nail. The wet paper will mould to the curved shape of your nail whereas dry doesn't (believe me, I tried!). Make sure to really push it down though (your base coat shouldn't come off onto your wet finger).
Once the base coat is dry, put lots of thin layers of top coat clear polish on. I did three, making sure to let each one dry between applications. Three made mine solid as a rock, but keep going until you can no longer feel a distinct ridge where the paper starts.
When it's time to remove them, simply soak a cotton ball or pad in nail polish remover, hold it tight over the nail, and after a minute the paper should peel off and the base coat can be removed as normal. If not, just scrub until it does peel off!