This is about women, but I think the same goes for men: always ask for a lot more money.
Our process, despite the pay gap, is identical for men and women. We start with phone interviews, and move into a personal and technical interview. Once a candidate passes both of those, we start salary negotiations. This is where the women seem to come in last.
The reason they don't keep up, from where I sit, is simple. Often, a woman will enter the salary negotiation phase and I'll tell them a number will be sent to them in a couple days. Usually we start around $45k for an entry level position. 50% to 60% of the women I interview simply take this offer. It's insane, I already know I can get authorization for more if you simply refuse. Inversely, almost 90% of the men I interview immediately ask for more upon getting the offer.
The next major mistake happens with how they ask for more. In general, the women I have negotiated with will say 45k is not enough and they need more, but not give a number. I will then usually give a nominal bump to 48k or 50k. Company policy wont let me bump more than 5k over the initial offer unless they specifically request more. On the other hand, men more frequently will come back with a number along the lines of 65k to 75k, and I will be forced to negotiate down from there. After this phase, almost all women will take the offer or move on to somewhere else, not knowing they could have gotten more if they asked.
At the end, most of the women I hire make between 45k and 50k, whereas the men make between 60k and 70k. Even more crazy, they ask for raises far less often, so the disparity only grows.
Once they've decided to make you an offer, asking for more money won't make them rescind it.
(HT: Susannah Breslin.)