To a first approximation, you have two ways of negotiating for a higher salary, namely fairness and leverage from other offers.
If your offer is not in line with what other people have received under similar circumstances at the same institution, then you can ask them to address this. If you make a convincing case, they may improve the offer, either out of a desire to do the right thing or out of fear of embarrassment if the details became known (for example, if it suggests discrimination). However, it's rare for there to be enough information to make an objective case for unfairness. Unless the offer is really outrageous, you aren't likely to have much success with this sort of argument: probably, the administration will just explain why they think it's fair.
By far the most successful way to negotiate is based on other offers. This gives you concrete proof that another university values you more than this one seems to, and you can make a credible threat of going there instead. You can't necessarily expect to get other offers matched exactly, since the comparison always involves a complicated mix of benefits, cost of living analysis, departmental quality, etc. However, it at least gives you a powerful way to start the conversation, and you'll have a lot of leverage if you might plausibly accept the other offer instead.
Incidentally, the worst mistake naive job candidates make is to accept a job offer and then try to negotiate. During the period when you have offers but haven't accepted yet, you are in a better negotiating position than you ever will be later. As soon as you accept, almost all your power disappears.