If we design a logo for a client and send it to them, how do we make sure they are not scammers?

Is this the original work? Or has it been edited (by Illustrator's Live Trace for example)?

Anyway, you may do as the people in this woodcut in case you think someone scammed you somehow.

Get the work deal done in writing, be it a contract, written purchase order, etc. Like Monika said, give the client low resolution pixel-based proofs to view. It might even be a good idea to bake a layer of water-marking into the image for good measure. Splitting the payment for the work into two or more payments is also a good idea (such as a down payment to start work and then the rest of the balance upon completion).

The only way I might agree to do freelance work for anyone on a verbal basis is if the person lived in my city and I knew them already. Even in those cases "the good ole buddy" can still sign a written proposal. It's common for business people to attempt sweet talking someone into letting down their guard and getting work done informally. They'll pretend they're your pal and then may try very hard to never pay you for your work.

That's what contracts are there for. If you don't trust them, don't work for them.

Apart from that: while in the process of making the logo: send them low resolution bitmap versions.

You can also have them pay parts of the sum in steps during the process.

And then: Why should they edit the logo? That makes no sense anyway.