How can I begin to interact with other players such as teams and chat and stuff? I'm kinda new at online gaming.
You should be default set for open teaming, which means that sometimes when you enter an area on a mission map you might automatically join a team of people already there. You can also search through the available teams lists to see who wants to play on a team for missions or PvP.
Other than that, you're just going to have to find some friends. E.g. try looking in the fleet recruitment section of the forum to see if there are any players with the same kind of values you have. Or if you see the same people over and over in the game, try chatting with them and send a friend request.
But don't friend spam people - like sending a friend request to a stranger because I hate those I ingore strange people like that.
Or perhaps participate in Zone chat - the chat channel where everyone where you are currently located is talking in - e.g. everyone in Gamma Orionis is just calling out all the time in zone chat looking for people to team up with on special task force missions.
Adding onto the post above me, you can also type "/who" to see who is in the same instance as you, then you can private message those people and such to talk to them, add them to a team or get their info by right clicking on them.