There are a few components to being a good "negotiator".
1. Put yourself in situations where you're comfortable walking away. If you're frequently finding yourself in back-and-forths where you're afraid of the other side saying no, you may be putting too much on the line. Start off with lower risk negotiations, and slowly ratchet them so that you have something to fall back on.
2. A lot of people think that negotiation is a "fight" to arrive to get what you want, but the reality is more complicated. It's really a joint agreement where both sides get most of what they want. Most negotiations rarely end with all parties feeling getting everything they desire. To achieve this, communicate your needs clearly, and likewise, try to understand the other side's needs. Only then can you make demands that make sense.
3. This goes along with #1. It's very important to give the sense that you have control over the situation. In a salary negotiation, this could be having multiple offers, or very clearly communicating that you don't need the job. In a PR, it might be replying to pushback on a change by explaining in detail why it's a positive for the codebase, and throw out a few architectural details to support your statements. If you're trying to get an upgrade during your hotel stay, usually just asking is enough—most hotels are fully booked anyways, so as long as you appear calm and deliberate about it, you'll probably get something extra.
4. I hesitated in adding this as a specific bullet point, since it might be "controversial"; be nice! You're dealing with humans, not machines. Don't be rude while negotiating. It rarely works out as a strategy to get the other side to concede. Nice people are fun to work and deal with.