function onClicked()
local c = game.Players:GetChildren()
for i = 1, #c do
c[i].Character.UpperTorso.CFrame = CFrame.new(script.Parent.Parent.L8.Position)
end
script.Parent.ClickDetector.MouseClick:connect(onClicked)
L8 is a part name in my game. When one player clicks on the teleport pad it teleports everyone ingame to L8 (the part) when we only want the person who clicks it to teleport. It's a two-way teleporting system and the parts are contained within a model.

2 comments
SuperMario's script is what ended up working for me (since your script made welded parts fall off of players, which we need for our game) but thank you for the thorough explanation!
No problem, also, it was because I moved the entire character model and not a part inside the character like what SuperMario did :)