Well I published a few print-on-demand books through Amazon. Start by making an account at Kindle direct Publishing, which should be here: https://kdp.amazon.com/en_US

Then it's just a matter of uploading the electronic files for the cover art and interior, ordering yourself a proof copy (which is really cheap) to make sure everything looks perfect, then list it for sale. You can also order copies for yourself that I think are the same price as the proof copies to distribute yourself. One thing I found is you cannot use the same electronic copy of your interior for an eBook, the formatting is different. There are templates available for download to help getting the format right. Go ahead and make yourself an account and let me know if you run into any problems.