Negotiating for a faculty position can be a stressful experience. There is a lot riding on decisions made in a short span of time. Fortunately, you can get everything in writing and make sure all is well with a simple rule of thumb: chat on the phone, negotiate via email.
Many people think of negotiations as this high-pressure back-and-forth game where you are sitting in a room, gauging their reactions, and adjusting your strategy on the fly. That’s not the way it goes in veterinary academia. We are refined, dispassionate, and professional.
The hiring manager (typically the department chair) will either call or email you with an offer. If they call, there will be a little chit chat and they will tell you they would like to extend you the offer. They may or may not bring up salary at that time. Your response on the phone is: “Thank you very much, I am very excited by the prospect! Please email me the details to look over.” Ideally, they will then send you an offer letter including commonly-asked-for items (e.g. FTE, moving allowance, startup funds, etc.).
Once you review the offer, consider what you would like to counter with, if anything. If you are happy with the offer, you can reply via email to that effect and then a signed contract will be created. If you want to negotiate, you can reply via email with a list of requests to made to the offer.
The phone can be used to ask or create clarification, if necessary. If the negotiation is complex, or some items you are asking for may be controversial, a phone call to discuss your reasoning may be helpful. Conversely, if the institution is unwilling to give you something you believe is reasonable, a phone call may help clarify things. For example, if the institution will not pay for a housing scouting visit, it may be because that is an institution-wide policy. A quick phone call can clear up any confusion.
I strongly advise against negotiating, in real time, on the phone. Firstly, this is stressful for you and for the hiring manager. Secondly, the hiring manager may not be able to negotiate some of the items you are asking for- it needs to get kicked up to the Dean in any event. Finally, you want everything in writing. The most frustrating experience would be getting a verbal commitment on something important but not seeing it show up in the final offer letter.
So, the rule is simple: chat on the phone, negotiate via email.