What are the mechanics of negotiating a faculty job offer?
I'll assume this is for a permanent, not a temporary or part time position. 

Unfortunately, there is no general advice that would be applicable everywhere. The US doesn't have a national system for such things, nor even one that applies to any single State. You may have a lot of flexibility or very little. But if the offer lays out a lot of things then you probably have less wiggle-room than if it only says a bit. 

But you may get at least a promise that they will try to accommodate the needs of a new member of the faculty. Not too many preparations is a good thing to talk about and most universities will probably try to do that anyway, but it is hard to guarantee. Funding for travel is another thing to explore. But, you may not get any guarantees. 

On the other hand, nearly everywhere will have an interest in bringing on a new member of the faculty smoothly and not inundating them with scut work. You might get a pass on committee assignments for a while. You might get a "promise" that you can teach in your specialty. But, depending on the size of the place and its main focus, the constraints may be strong. A large place with a research focus and lots of TAs probably finds it easier. 

I was once at a top university where a lot of things were arranged around helping a young newcomer to the faculty advance her research agenda by inviting post-docs whom she favored. I was very impressed that the "old codgers" on the faculty were so supportive of a new person. But this is, I think, an outlier. Not every place can or will be so accommodating. 

I also once negotiated a promise that the university would cover rather extensive international travel. I swapped a bit of salary for that, but everyone came out happy in the end. 

If you want to negotiate, it is very useful if you can do it in person, probably with the program chair or even a Dean. If you can be flexible about some things, then, perhaps they can be flexible about others. Deans often have some pot of money they can use for such things. They also have a bit more flexibility with "bending" policies. 

At the other end of the scale, I doubt that very many offers are "take it as is, or leave it." They will talk to you, nearly everywhere. 

Yes, after you come to an agreement, a contract needs to be signed spelling out everything. You will probably only have a short time in which to sign and return it.