You have a couple options here:
1) You can save the file you want to print onto a flash drive and then take it into Staples and they'll print it off for you. If it's not a common document type, you can save it as a PDF and take the PDF with you.
2) You can log into the Staples online printing centre (staplescopyandprint.ca), upload the file and tell them which store to print it at. They'll print it and you just go pick it up. I use this if I'm doing a presentation out of town. I print all my hand-outs at the Staples where I'm doing the presentation and pick it up when I get there instead of lugging the printouts on the plane with me. Works really well.