Sorry if this has been answered before, but I googled this question and found only 'import save file' links and nothing answering my question. Can I transfer my current run from one computer to another? If so, how do I do that? I play through Steam if that matters.

If you use steam the cloud saving should automatically transfer saves for you. Just to be save you might want to copy saves from the game folder (C:\Users\{your username}\Saved Games\Pillars of Eternity Deadfire) and have them ready to copy into the same folder if for some reason cloud won't automatically import.