You can usually find a link to downloading / printing your own copy of each month’s postcards over on The Main Page. Find the month you are curious about, and download the image. You might not need to print them out, but you will need something connected to speakers that can activate the code.
But the best way to enjoy a postcard is to join the mailing list:
Make sure to add to the subject line, “I’d like to join the mailing list,” or something like that. The bots are pretty good at parsing things, but you should at least mention a mailing list, and wanting to join it.