You'll need to purchase a stamping kit, something like this:
(Always finding the good bargains!)
The concept is pretty simple- you paint polish over your chosen design on the stamping plate.
Scrape away the excess with the scraper
Push the stamper down onto the design firmly
Push the stamper down on to your nail.
It can be tricky to get it right straight away- polish consistency will change things a lot, and you have to be quick between each stamp as it will dry out. It can also be difficult to get the placement of the stamp quite right aswell, but it'll come with time!
Here's some examples of my nail stamping:
And if you're interested in what polish that is, check out my favourite polishes post :)