Yep, the problem was indeed with the putty under the flange. BUT, I only found that out when I tried to loosen the retaining ring/nut. I lightly tapped the ring on one of the protruding things on the side and was able to turn it by hand. Unfortunately, the reason it turned so easily, was that it, along with the gasket, had deteriorated and just fell apart. There's a nut further down on the straight drain pipe which is on there pretty solid which I don't think I can get off, so I'm just going to remove the nut on the other side of the trap, which I can loosen, and replace everything. If that doesn't work, then it's on to plan 'B': call someone who actually knows what the heck they're doing so I can use the sink!
By the way, I did search on google, but there really wasn't all that much on this, at least that I, with my limited knowledge, was able to comprehend.
I'll probably make another appearance here before I'm done!
Thanks for the input.