My advisor's wife is having her first baby and he told us about it at our last lab meeting. We understand that this will mean he might need extra time/patience as the big day approaches, but are we supposed to be doing anything else? What is the etiquette for this as one of his students? Should we be buying him some kind of baby gift?
A personal gift from you, as an individual student, is not expected, at least by European or North-American etiquette. It may be nice to pool with other students and group members to offer a small gift (either something for the baby, or something for the father). It'd be more customary to offer it after the baby is born, rather than now.
On the other hand, there is no strong expectation that you offer a gift. I.e., if you decide not to for any reason, he won't think it weird.
I completely agree with @F'x's assessment: no gift is necessary really. Having said that, if there's something you can do that's simple and doesn't strain your budget, then as a courtesy (from a colleague to another) that might be welcome.
Having been in this situation myself (from the advisor's side) I can say that one thing parents of a new child lack that grad students might have more of is time. If it's possible, lab folk could offer to help running meetings without the advisor, do guest lectures in classes if it's appropriate, and so on. Again I emphasize that it's not necessary at all, but it's a gift that would not cost you money, and would be greatly appreciated by someone who probably isn't sleeping very much :)
This is the same answer I gave about weddings but it holds for births also.
You must do something. Building social relationships with your work collegagues is really important. If other students are organizing the collection and suggesting an amount, I would give that much. If they are organizing the collection, but not suggesting an amount, I would chip in two beers worth of cash. In some cultures two beers will be on the generous side, while in other cultures it will be on the cheap side. It won't be out of place in any culture. If no one is organizing the collection and you want to take charge, then I would suggest asking people to chip in one beer worth of money (all students should be able to afford this). If no one is organizing a collection and you don't want to take charge, go out and buy a card and get the other students to sign it.
Buy a book for the baby. That is an appropriate academic gift, and it doesn't threaten professional boundaries.
Of all the gifts we received after giving birth or adopting, the one that meant the most to me was from a children's librarian. She gave us a card congratulating us on our adoption, along with a book, Pat the Bunny, that came with its own small stuffed animal that went along with the bunny in the book.
Any activity book for the really early stages of reading a book to a baby would be good. For example a book that has holes in the pages, for the parent to stick fingers through the holes to simulate one or another animal, is good. Or one of those books that has texture materials glued in. If you go to a bookstore you can ask the clerk for the section with books for babies.
I personally found that the books with the finger holes, or the texture materials glued in, made more of a hit than the vinyl books that were safe for slobbering or bathing. A book with sensory and theatrical capacities is the best first book, I think.
It's true that a book can't be used right away, but that means that your gift will be remembered longer than the pacifier or the rattle.