As mentioned in other answers, it's completely fine to use / extend ideas from a preprint that's been posted on arXiv or otherwise made public. This is essentially the exact reason why the author made the preprint public in the first place. You will cite the preprint as you would a paper published in a journal, conference proceedings, etc, except that of course you will list an arXiv ID instead of a journal title, volume number, etc. Your journal's style guide should explain how to cite preprints (if using BiBTeX, consider @preprint).
You may convey additional thanks in your Acknowledgements section if you are moved to do so, but this should not take the place of proper citation.
Of course, as is the case whenever you are extending someone else's work, your paper should accurately describe the work done by the preprint's author, and carefully distinguish it from what you have added. You should be careful that you do not inadvertently misrepresent the preprint author's work as your own.
There are a few extra considerations when extending work from a preprint:
Keep in mind that the preprint has not undergone peer review. Of course, peer review is no guarantee of correctness, and if you are writing a paper that depends heavily on a previous paper, you will want to check it carefully enough to be sure that your work rests on solid foundations, regardless of where/if the previous paper was published. But for an unreviewed preprint, you should check it even more carefully.
Before starting work on your own paper, you might want to consider contacting the preprint author with your idea and suggesting a collaboration. In addition to sharing expertise, this also helps mitigate the risk that the preprint author has already had an idea similar to yours, and is currently writing it up in a paper that will be published before yours would be. (This is also possible when extending work from a traditionally published paper, but is perhaps somewhat more likely in the preprint case because of the shorter timeline; if the work is very recent, it's more likely that the author is still actively working on related topics.)
There's a good chance that the preprint is currently being reviewed for traditional publication. Before submitting your paper, you should check to see whether the preprint has been accepted / published in a journal / proceedings / etc, and update your citation if necessary. (If it has been accepted but not yet published, you can list it as "To appear" with the journal's title.) Check one more time when you correct the galley proofs of your paper.
Check periodically to see if the preprint has been revised or updated, as the changes may involve something that materially affects your paper. Note that arXiv only includes the first 5 updates in their daily emails, so just checking the emails may not suffice. It is even possible for an arXiv preprint to be withdrawn by the author (this might happen if they find a fundamental error); it remains available for download, but in this case it's probably not a good idea to try to use it. (Of course, published papers can also have corrigenda or retractions, but they are more common for preprints.)
