I bought a used iPhone on ebay. when I try to activate it, I get a message that the owner needs to sign in to the device with their appleID and password. I have no way of knowing who the owner is. How can I get around this?

There is no way around it. Return the phone for a refund.

Check the eBay listing. Did it state the device was Activation Locked? If not, then make a claim as Meg stated and get a refund. You will not be able to activate the phone and no one can help you contact the owner, unless that is the person that sold the device. If they cannot remove the phone from their account because it is not theirs, then refund is your route. Even Apple cannot assist with locating the previous owner.