How can Naruto characters teleport/disappear? In the manga/anime, it appears as if teleportation is very rare. The few we know that gets a little bit explained are, for example, Minato (4th Hokage) and Obito (Tobi).

Despite of this, a lot of characters (mainly in the anime) "disappear" with a flashy exit when they wish. Orochimaru does this a couple of times, including others. Often with a phrase such as "I don't have time to play around with you any more" and then poof, gone!

Is there some explanation to this? Do they use a clone and then run off while the clone says goodbye to the opponent? If that is the case, when do they create the clone?
From what I understand, there are only actually a few ways to teleport. Those include Tobirama/Minato's Flying Thunder God technique, reverse summoning, and Obito's space/time Sharingan based technique.

Most of the time, when shinobi just poof, that means it was either a clone or they travel at a high speed such that one can not detect their movements. If it was a clone, then it was always a clone to begin and the person did not just substitute himself for a clone.