I haven’t been directly involved in a contract negotiation, but I’ve listened to my union leadership talk about the bargaining process enough to pick up on a few things:

• Check and see if you can find out what similar unions in your area have won out of their most recent contract. It will both give you a baseline of what you can reasonably expect, but also may be what management themselves will use as precedent so you’ll be prepared either way.
• Management offers often have a way of being presented in a similar manner as a slimy car salesman trying to pull the wool over your eyes with a great-sounding monthly rate that’s actually more expensive in the long term. Be prepared to run the math on their offers and counteroffers, especially when they say something like “well we can’t give you X, but we’ll give you Y which is better” as often it sounds nice but the math doesn’t pan out. This is particularly an issue with signing bonuses as they sound great to members, an extra grand in my next paycheck!, but you might run the numbers and see that the benefit you had to give up for it would have saved your members twice that over the life of the contract.