When you bid on something that says "no shipping", then the seller has to pay for all shipping costs. Most of the time, the seller will add shipping costs though. You might find some who don't, but they usually will add shipping costs. Also, you can browse for certain things and specifically check the "free shipping only" box so that you will only be looking at items posted that you will not have to pay shipping on.
If there is a shipping cost listed, that means that the bidder will have to pay it to the seller via PayPal after the auction ends. Once the auction is over, the seller will send a private message to the top bidder with their PayPal email address and the highest bidder will send the seller the address they want the item shipped to.