How do you teleport a part to a character?

It's close to being correct, but in roblox, you use vectors for positions and forces.

local hit = game.Workspace.WiseDumbledore.Torso.Position
game.Workspace.Part.Position = hit --Since 'hit' is already an vector, you don't need to use 'Vector.new()'

If you want the part to get moved to that exact position, ignoring the fact that there are other parts in the way, you use coordinate frame variable(CFrame):

local hit = game.Workspace.WiseDumbledore.Torso.Position
game.Workspace.Part.CFrame= CFrame.new(hit)

I think it would display an Error. You haven't specified the player, instead, your hit variable is in Workspace, Players are not in Workspace. Line 2 looks correct.

Now it depends really, if you want this to be repeated, you need to add a loop. There are many loops. The while true do loop makes it go forever. I am not so familiar with other loops, since I need to revise them. If you wish to do the while true do loop, the following code should be correct:

hit = AAA -- First of all, Find the player's TORSO... Replace "AAA" With the Torso's Path (eg: game.Players. etc...
Part = Workspace.Part --The Part that you want to teleport

while true do --Keeps this going on forever
Part.Position = Vector3.new(hit.Position.x, hit.Position.y, hit.Position.z) --You forgot the Vector3.new().
wait() --Add how many second it should wait before moving again. Or leave it, so that it doesn't crash.
end

--[[ NOTE:
Always leave a "wait() " in the loop, or else Studio WILL Crash.]]

No, it is not correct. Position is a property of BasePart, but WiseDumbledore is a Model, a Model does not have x, y, or z as Properties.

What you should do is get the position (a Vector3) of the Torso (a specific part of the Character) and then you can assign it to the Part that you want:

positionOfTorso = workspace.WiseDumbledore.Torso.Position
workspace.Part.Position = positionOfTorso

Alternatively, you can set the CFrame (CoordinateFrame) of the Part and this will allow you to put parts inside each other (i.e. instead of placing the Part on top of the player)

positionOfTorso = workspace.WiseDumbledore.Torso.Position
workspace.Part.CFrame = CFrame.new(positionOfTorso)

... or you could just do it in one line by referring directly to the CFrame of the Torso

workspace.Part.CFrame = workspace.WiseDumbledore.Torso.CFrame

Hope that helps!