Teleportation is a term given to the act of moving a group of Parts (most of the time, a player's character) to a certain coordinates. In ROBLOX, setting the Position property of Parts would disconnect the Part from any other connected Parts and break the model. Therefore, one cannot use the following to teleport a player because it would disconnect the Torso from the Head.
To correctly teleport a player without killing them, you must use the CFrame property and use the CFrame data type instead.
MoveTo can be used in place of setting the CFrame of one brick in the model. MoveTo will only change the Position/CFrame of the Parts in the model if the Parent property is the Workspace.
One can teleport all players in the game by iterating over each one of their Characters and setting the CFrame accordingly. However, you should be careful and offset the target positions so that the players' torsos do not overlap.
The above code would teleport each player to the position (0,50,0), going up 5 for each character so they do not overlap. If you place players on top of each other, make sure the area does not have a ceiling so players aren't put on top of a building.
You can add in fading effects by using for loops to set the Transparency of your limbs.