Anything you want! You can copy it, publish it, change its format, distribute it for free or for money. You can translate it to other languages (and claim a copyright on your translation), write a play based on it (if it's a novel), or a novelization (if it's a play). You can take one of the characters from the novel and write a comic strip about him or her, or write a screenplay and sell that to make a movie.
You don't need to ask permission from anyone to do any of this. When a text is in the public domain, it belongs as much to you as to anyone.
(However, when some character or part of the work is also trademarked, as in the case of Tarzan, it may not be possible to release new works with that trademark, since trademark does not expire in the same way as copyright. If you propose to base new works on public domain material, you should investigate possible trademark issues first.)