When I open finder, there is a shared computer listed that is unknown to me. Can I delete it, or identify who it is?

Just drag the entry out of the Finder's sidebar. If it's simply a nearby neighbor's computer being picked up via wireless, then it will probably just reappear.

It won't drag. Right click only offers open or get info. Delete key is useless. I don't have wireless turned on on the machine (hardwired to router), and it doesn't look like a neighborhood machine.

If I click on 'connect as' it says that there was a problem connecting....

Check the server name or IP address... and try again.

How do I blow the blasted thing away?

Try going to Finder preferences > Sidebar > Bonjour computers and uncheck it

Do you have a printer with a card reader? What make?

Likely just your printer, like my HP:

Did that - will see if it works. It wasn't there today. Printer does not have a card reader

I have a HP wireless printer. How do I find it's number like you show in your screen shot?

In Finder>Menu Bar>Go>Network it should show

You just saved my evening! Thank you,sir.