This is it, the job offer. All your hard work has paid off and the employer wants you as part of the team. Your job is not finished yet though, now you have to get yourself the best deal without losing the job offer.
Whilst every negotiation has its own feel, here are some points to consider:
If you are talking on the phone and restricted in what you are able to say (eg, you are in your current employer's office), tell them that you will call them back. Negotiating a contract when you can't say anything is definitely going to hamper your style and stop you getting the best deal for youself.
Don't be blustered into something you don't want to do. Try to remain calm and think things through before agreeing to anything. Asking them if you can think about it for a little while might be a good idea. This even gives you the opportunity to run your thoughts past someone else in the mean time.
If you are still in an existing job, it can be a good idea not to hand your notice in until you have signed a new contract. You have a balance this up with whether you might be able to swing a better deal with your existing employer. If you back down on an agreement, you can end up tarnishing your reputation around town. This may hurt you in subsequent job hunts or even your existing position.
Try to clarify as many things as you can before agreeing. If you have already agreed and then start asking for changes, you are fighting a battle on much weaker grounds.
Check things like insurance policies, tax rates and such, don't just assume the standard policies will apply. Ask friends for ideas on what might be wise to ask your potential new employer.
Good luck and enjoy your new job!