Negotiating Teaching Assistant salary, I heard from an administrator of a different grad program than mine that TA salaries are in fact negotiable -- a little known fact to be aware of.

Given this tip, how can I effectively negotiate my pay for the classes I will TA for, before signing my contract with the human resources department?

Unlike in industry, I don't have TA salary information from, say, other schools around our campus location to make an effective argument for more money.
In general, TA salaries are not negotiable, but are instead set by a department or school for all students. There may be some "wiggle room" in special cases: for example, if you have already served as a TA and have experience, there may be a higher level of pay available under such circumstances.

In the event that your school allows for negotiations, I would say in any case that you would have to provide a solid argument for why you deserve more than the standard salary. Do you already have teaching experience? How much? Where?