You do not have to have a printer to use the site or send your books. You can hand-write the address on your package, if you don't have access to a printer. See Can I hand-write the address to send a book?
The only PaperBackSwap feature that you will not be able to use if you do not have a printer is the optional Printable Postage feature.
Getting/Printing the Address to send a Book
Can I hand-write the address to send a book?