With things like that, it just has to be creatively distinct, which tends to be the most important part of avoiding copyright infringement. Care has to be taken to bring something new or different that someone else isn't doing, which doesn't interfere with their ability to benefit from their creation.
It's a little complicated, and it's part of the huge mass of problems with copyright, when considering things being basically re-copyrighted. But the thing to remember is this: if the original concept is in the public domain, you can use that original concept as you like. However, you must be mindful of what other people have done with it, so you don't accidentally retread what someone else has done.
If the concept in question is, say, Cthulhu, you can use what of Cthulhu was established by Lovecraft's writing and work from there to develop your own creatively distinct Cthulhu characterization. However, if an author named Mrs. Gablefinch had written a series of books establishing that Cthulhu was definitely from the planet Blard and had three children, each named Lasseh, you would have to find out if Mrs. Gablefinch's work was in the public domain in order to use it. If her work isn't in the public domain, you would want to avoid mention of a planet Blard, and you would probably get in a little trouble for including the three Lassehs.
It's just made a little more complicated because some people have already worked with things in the public domain (and sometimes even before they were established as being firmly in the public domain), so there are some touchy territories. It is important to point out, though, the difference between a copyright and a trademark, which are very different things indeed.
