When playing RPGs, it's important to know the people you are playing with, who they are as people. By recognizing their play styles, you can cater your play to their strengths. It doesn't matter if you're the GM or another player. In doing this everyone can have a better experience at the table.
The most obvious aspect is how they treat others. In other venues, like work, meals, or hanging out, they may act one way. Once people get in game they may act differently. Are they working together with each other to play, or are some people trying to talk over others? When decisions have to be made, do they work on a solution, take control, or abdicate? Are there people who are quiet and not active in the game? Is the GM working with the players to succeed or are they a killer GM?
This leads to how people are acting in game. Are people getting deep in character, or playing with next to no role play? Are there specific parts of the game that are engaging people? Note how everyone is acting in combat or in investigative or dramatic scenes. Do the players and GM tend to focus on one aspect? Are people acting in ways that are inappropriate?
With this knowledge, reflect on what you've seen. If there is a part of the game the group enjoys more, try to find games that focus on that aspect. If combat is what players crave, try to find systems that focus it, like Eclipse Phase or Dungeons & Dragons. If people are more into investigation, try systems like Delta Green or Gumshoe. If interaction is what gets people excited, try systems like Fiasco or MonsterHearts.
As to the players themselves, how they play can help you play better with them. If players tend to work together and corroborate, you've got a great group. If they talk over others and try to be the center of attention, find ways so they feel part of the game but not hogging the spotlight. Spotlight other players so everyone gets a time to shine. If the GM is making things too hard, try to work with them to make the game something everyone can enjoy.
If there are issues where people are acting inappropriately, try talking to them in private or with another person. If it is something that can be corrected chances are they will be willing to work with you. If they don't, then maybe they aren't a good fit for the table. The throughline in all of this is communication. Talking with your fellow players before and after play can help you see what you all like and dislike and can improve your play.