Printing a pdf should be not different than printing anything else, regardless of what OS you have.

The apparent problem is just with finding the "Print" button to tell Windows 8 to print something.

I haven't looked for the specific instructions, but based on other things I have seen explained by Microsoft for Win8, I would suggest that you:

Wave your left hand from right to left over the display.

Swipe your right hand from bottom to top over the display, making a 90 degree right turn halfway up.

Tap the screen twice in the lower right corner.

Step back and spin around twice counterclockwise, followed by one full turn clockwise.

Stick your left thumb up your ass and hold it there while you bang your forhead twice on the middle of the display.

Go have a beer while leaving the computer alone in peace for a while.

Sneak up on it when you've finished the beer (Don't let it see you coming), and see if it's done something.

Leave the computer where it is and go teell all your friends how wonderfully it did whatever happened (which likely won't have had anything to do with printing anything, but will give you something really fun to talk about).

As a backup, your browser should be able to open a pdf, and with the pdf open in the browser you might be able to use the normal browser menus to print. This isn't an ideal method, and you'll probably still have to figure out how to open a file in your browser instead of in some other default program in Win8 so it's unlikely to be a lot of help; but it may give you another interesting bunch of questions to discuss with your friends.

The theoretical reason for pdf is that any printer that can print anything else should be able to print a any pdf, but since that theory originated with Adobe it may be no better than the recent stuff from Microsoft.

John