Together = attached, connected. In relationships, it means to be as a couple. "Are Dave and Jill still together?" "No, they broke up last week." It can mean for several units to unite and become one. If several wolves join together, this forms a pack of wolves.
It also must be mentioned that there's a common phrase: "To have your act together." It means that you function in a responsible way and can be counted on. "If you don't get your act together fast, you're going to be fired!"
Each other can basically mean ourselves/themselves.
"By working together, I think we can help each other." (I used them both in the same sentense to try to really show how they're used). This means that if we work as one unit, I think we can help ourselves.
"That team could be much better, but the players are greedy to score the most points and they do nothing to help each other play better." This means the players all want the ball to score the most points and they don't help themselves play as a team.