The biggest piece of working with anyone is to not make them wrong when giving feedback. The best way to do this is to ask questions. Ask leading questions that lead the person to figure out their own mistakes. When someone figures out that they are wrong on their own, they don’t dwell very long and they don’t hold a grudge.
It is also helpful to learn about people and their personalities. There are countless books about personality quadrants and the traits of each quadrant. Knowing these will make it easier to communicate with your peers.
When you learn about people and what drives them you also understand where they are coming from and you may be more sympathetic to why they did what they did. With understanding also comes better communication about how to move forward.
Additionally, when you feel the need to give feedback it is because you had an expectation of things being different. And when your expectation wasn’t met, you might be blaming someone else rather than examining your own expectation, why you have it, where it came from, if it’s reasonable, and if it has been communicated.
Feedback is a two-way street. The person giving it has just as much to learn from the feedback as the person who is receiving it. Make sure to keep the blame in check and simply communicate.