Stamps are big news in Japan. A person will often have a hanko or personal stamp, and you see shops and even vending machines selling these. You'll also find special stamps as you travel around Japan- each station you visit will have a special stamp and so will lots of other tourist spots.
It's a good idea to grab a notebook, or buy a special Eki Stamp book, or even a Temple Stamp book, because you'll find stamps along the way at temples too. A special book will be a little more expensive, but will make a lovely souvenir.
The spot where you can grab your stamp won't always be immediately apparent, but the station staff will be able to point you in the right direction. Plus, you'll get better at spotting the set up as you go.