Rust used to be much harder before they introduced the team system. It's been highly controversial, because the veteran players argue that the game shouldn't have the amount of situational awareness that teams give you.
Regardless of what you think about the system, the feature is very helpful for groups, since it allows you to easily distinguish your friends from your enemies.
To invite people to your team, you first must create a team in the inventory. Then, you need to walk up to them and press E to invite them. After they receive the invite, they need to go into their inventory to accept it.
This was the shortened answer, so I'll go into more detail to better explain it.
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Creating a team
You can create a team anywhere you want, just as long as you aren't in one already. The player that creates the team will automatically become the leader, but you can always change who the leader is later on.
The leader is also the only one who can invite other people, so make sure you choose the right member to be your leader.
To create a team, open up your inventory and navigate to the bottom left. You'll see that there's an option that says "Create Team," and clicking that will instantly make a team for you and your friends.
Sending an invite
Now that you have a team created, you need to let some people join it. You can only invite someone who's standing directly in front of you. If your friend is across the map, you can always create a sleeping bag and give it to them by clicking "E."
Once they are right in front of you, you'll see the option to invite to a team. Pressing "E" on this once will immediately send them an invite.
Accepting an invite
The easiest part of this process is accepting the invite, which can be done by going into your inventory and pressing "Accept."
Leaving a team
If for some reason you ever want to leave your current team, simply go back into your inventory and press "Leave Team."
For players who are the team leader, leaving the team will make someone else the leader if there are multiple people on the team.
Promoting to team leader
When you want to change who the leader is, simply walk up to another player on your team and hold "E." After the progress bar has filled up, the other player will become the leader.
