How do I go about negotiating an academic job offer?
To answer your question, according to some, the best time to negotiate is after an offer has been given by the potential employer. For one thing, they have already ruled out other candidates and they have now essentially decided on giving the position to you. The hiring process is arduous from their perspective as well and the last thing they want to do is to decline someone they have already decided upon because that person negotiated their salary with a reasonable increase.

You would need to know as much as possible about the expected salary before you could negotiate. The key to negotiation is always having sufficient knowledge. If you know that the offer that they gave you is not on par with other similar positions at that university/field, then you have something to point to. You can find salary information from sites like Glassdoor but more importantly, sometimes these are published by the universities themselves. For a lot of public universities, you can easily get his information by simply contacting the central finance department to get averages. In some cases, the universities themselves publish this information on their websites. A good tip to find salary figures is to search Google for:

site:theuniversity'swebsite "salary" "write the position here"
This will give you hits for all of the pages that mention a salary figure along with the position that you are interested in. Here is an example of that using Heriot Watt
site:hw.ac.uk "salary" "professor" 

That query gives a couple of results with actual salary figures.

You also need to state why you should be given a higher salary. Chances are that they have already budgeted to be able to increase the salary for negotiation purposes. You still need to provide a good argument for why you deserve a higher salary. Does your publication level/quality warrant a higher salary? Do you have documents showing that you've received accolades for your research or teaching? Will your involvement increase the profile of the department due to your research networks? etc