My grandfather grew up in Poland in the 1930’s when he became involved in leftwing political organizations. There are family stories that when my grandfather graduated high school, he left for a year to join the International Brigades in Spain. How would I go about trying to find any records of his time in the International Brigades or any other information of his service?
So, starting with the caveat that I'm not a Polish speaker and have limited knowledge of the archival resources within Poland (I've seen the Archiwum Akt Nowych and Zydowski Instytut Historyczny mentioned, but couldn't tell you what resources they hold), there's a coule of places that you can begin to check for documentation on individual members of the International Brigades online.
The easiest place to start online would be the SIDBRINT project at the University of Barcelona, which has the largest database of volunteers from across the world, with about 30,000 individuals covered at this point. The website is a little clunky, but you can search by name easily enough. The amount of information on each person varies a lot, but it should give some idea of where to follow up and find more information (particularly books and other published material, it's less good on archival documents). This should be enough to confirm that your grandfather did go to Spain, though if they enlisted under a different name (which was not uncommon) that might make it more difficult to be sure.
If you want to do some serious research, you can start poking around the archives of the Communist International (Comintern). This was the organisation that was ultimately responsible for organising and recruiting the International Brigades, and a lot of the internal documentation relating to the volunteers ended up in their archives in Moscow. The good news is that a lot of this material has been digitised, and can be accessed and browsed freely. The bad news is that it's not at all user friendly...
First of all, the website is only available in Russian. If you don't speak Russian, I'd recommend using the google translate plugin available on Chrome to automatically translate the website, which gives you enough of an idea to navigate it. The bit of the archive you want is Fund 545 (http://sovdoc[dot]rusarchives[dot]ru/sections/organizations//cards/94999 - you'll need to spell out the [dots]; Reddit thinks the site is spam and blocks direct links). From there, if you're after personal information, Inventory 6 is the first place to start, which is where they have the files on individual volunteers. These files are grouped by nationality - Poland is folders 630 through 812 (the most useful stuff is from 677 onwards), organised in alphabetical order by surname (so for example the last folder is volunteers whose surnames start with Zum- and onwards). The actual documents could be in a variety of languages - Polish, Spanish, French or German being the most likely. But if your grandfather was in the International Brigades, odds are that you could find quite a bit of information about them in these files.