Great! Here are a few tips from me, not just for women, noting that I am going to skip over the super-important "make sure you are in high demand" kind of advice. I am assuming you already have an offer in hand, and wish to make the most of it.
1. Make sure they have made you the full offer before responding in any way, other than with polite enthusiasm. That means salary, teaching load, moving expenses, faculty housing options, length of contract, research and travel fund, and anything else you might care about, such as a joint appointment. Don't respond to any one bit of it until you have drawn out all the blood from the source.
2. You don't have anything until it is in writing. Duh.
3. It is fine to ask the departmental chair what else you might ask for. In such matters the chair is usually (but not always) on your side. In any case, this is not a faux pas.
4. Very often the components of your offer come from distinct pools of money or resources, controlled by different agents. You want to "tap" on each and every part of the offer, to see if it might be flexible. Inflexibility on one part of the offer does not have to mean inflexibility on all the other parts. Different pots of money! So ask for more along all margins, but do so politely. Rudeness doesn't help with these kinds of bureaucracies.
5. In most situations you can get a small amount extra by bargaining over the salary, and indeed you should. But you cannot get much more unless you have a written offer in hand from another place for a higher salary. Recognize your limitations. And a higher salary offer from a non-academic source often means zero in this bargaining game. You can't expect anything close to a match. At best it will be an excuse for them to bump you up a few more thousand dollars.
6. It is fine to ask for a semi-formal commitment on what you might teach, but do not expect this to be put in writing. Odds are it will be honored, but not 100% for sure. "I would like to teach in your honors sequence" is a perfectly legitimate ask, if appropriate to the situation.
7. Always ask for a course off for your first year, at the very least. And learn what will be the future rate for buying out of courses.
8. Most generally, while you should always be polite, "them liking you" is not an outcome you are looking to achieve at this stage of the game. They can like you plenty later. Probably you should feel just a little uneasy that perhaps you are asking for too much.
9. As for women in particular, there is a literature suggesting that possibly women do not bargain hard enough in the workplace. Whatever stance you take on this broader question, if you are a women at least ask -- and check with some mentors -- as to whether you are making this mistake. Actually men should do this too.
10. You do have a limited ability to ask for an extension on your offer and when you must say yes or no. But do not think you can stretch this too far, and it is often not in the interests of the school, or for that matter the department and chair, to give you much leeway here. Basically you want to do this to drum up a better offer from elsewhere, and they know this.