Hold LMB on another player and select the arrow with 3 dudes. A big arrow will appear over their head, indicating that you are following them.
They will know that you are following them when they look above your head: they will see a small, yellow chevron above you.
To follow someone into the wasteland, you gotta stand close to them when they enter the exit grid. The big arrow over their head will be bright when you are too far to follow them into the wastes, and dark when you are close enough.
The person you are following will be warned by the game that someone is following them with a warning sound and a red text message. You will appear on the list on the left side of the world map interface, right below theirs. They can either allow you to follow them (or not notice you) or kick you out of their group.