What do you guys do when you have a black or dark background you need to put your image on? For example I have a logo to put on a black background but you'll be able to see the white frosting sheet around it. Any ideas?

I had this same problem when I put a Washington capitals white edible image on a black round cake to look like a puck.It was a mess.I ended up taking it off and doing it with my projector in icing instead...The black icing looked blotchy underneath the image.It never did look melded.

What about puttig the image on a very thin layer of white fondant that's (precut to the exact shape and size of the paper) and letting it airdry for a while, and then put the fondant piece on the cake.
HTH

A lot depends on the type of icing sheet you are using. Our premium icing sheets are a bit thicker and while they are a bit opaque, they work better then the thinner brands. I have put images on chocolate with our premium brand and they have worked fine.