Negotiating can be one of the more stressful aspects of purchasing or selling a home. Many don't know where to start or simply don't know what the leverage points are for negotiating a transaction. If you've never done it before, you don't know what to ask for and what you are likely to get.
Negotiating power depends a lot on the market and the level of need on both sides of the table. It is common for buyers and sellers to get emotional and passionate about offers and counters that aren't what they want. Keep in mind that in a negotiation each offer and counter is just that. It's a starting place, a move on the board. It doesn't mean that is going to be the final outcome.
There are a few phases that we see buyers and sellers go through with each offer or counter.
1) Shock - It is not uncommon for an offer to be less than what a seller wants. The gap in expectations can cause a strong reaction as a seller immediately conceptualizes what it is like to accept the first offer. Emotions can run high and the seller tries to imagine changing their plans and coming to terms with the loss of purchasing power that the sale at their original terms would provide. This phase can take anywhere from 5 minutes to a few hours, sometimes overnight to run its course.
2) Acceptance - After a cooling off period, the seller is now considering if this will work at all or there is some middle ground to be had. Emotion gives way to prudence and the work of finding a solution can begin.
3) Strategize - There is always a line that the seller cannot cross, but you want to get as far away from this line in your favor as possible. Here is where you come up with several options, all of which are viable. The insight here is that providing choices gives the other side of the transaction the illusion of control. If you provide choices that all work for your side, then they are all wins.
4) Measured response - When making a counter, never blame or talk in absolutes. That will cause digging in and resistance. Using phrases like 'it seems like...' paint a picture without accusing. This gives the other side a chance to respond without being blamed. Instead make counter offers so that the other side can win too, or be wrong with dignity. No one likes to lose, so both sides need to feel like they got something out of the transaction. If your terms don't allow that, you are less likely to get what you want.
Money is also not the only metric for success. Think in terms of what the other side needs to achieve in their life. In many cases time, exceptions, or creative approaches can be used to solve pain points that are not just cash.
For further reading, these are terrific books and courses on the subject.