When offered a position, the first thing you should do is express your gratefulness to the offer. Even if you are holding out for a better offer, even if the offer is not at all what you wanted, thank them graciously, and ask how much time you have to make a decision. You want to avoid mentioning that you are waiting for an offer from a different firm, or are unhappy about their offer. Simply say thank you, and tell them how much you appreciate their offer to you. Then hang up the phone, and take some time to digest what has been offered to you, and how that stacks up with what you are willing to accept.
Some law firms will give you their first and last offer up front. That is because some firms have lockstep salaries for associates and/or strict formulas for determining partner salaries. If you are lucky enough to be working with a recruiter, they should be able to tell you what kind of a firm you are dealing with.
The next thing you need to do is determine whether you would take the offer as-is. Again, if this is a firm that has made you a take-it-or-leave-it offer, this may be the end of the inquiry. However, if you determine that the firm has some wiggle room, you need to decide whether you will ask for something more, and whether getting more will make or break the deal.
If you decide that you would like some extras but will do without them (moving expenses come to mind), I suggest asking (or having the recruiter ask on your behalf) for those extras while making clear that you are not rejecting their offer. You might be surprised how often firms will throw in extras they have not offered, even when the candidate is willing to accept the offer without the extras. This is a firm that wants to hire you, and they want you to be happy. They will generally do what they can to see that that happens. Therefore, do not be afraid to ask for extras if you want them, but make it clear that you very much want to accept their offer.
The harder scenario is when the offer is not at all what you had contemplated. I have had many candidates tell me to simply turn down an offer because they didn’t like it. This is almost never the best course. Instead, if you are prepared to walk away, why not ask for what you want? You don’t have anything to lose, and you may have something to gain. Firms will often do what they can to attract you to the firm. Things like moving expenses, better life and health insurance and health savings plans, a higher base salary or higher incentives or percentages for partners, a draw or salary guarantee for a limited period- these are all things that many firms expect you to negotiate. Some firms even offer free or tax-deductible parking. You need to ask yourself what is really important to you.
It is never a good idea to be combative, and negotiations are often delicate. If you are working with a recruiter, your recruiter can and should conduct these negotiations on your behalf, after educating you about what options are available, and learning from you what you would like to ask for. If you get enough of what you are asking for, you may just end up accepting an offer that you would have turned down flat.