How Do I Make A "Part" Looping Animation?

Did you mean move from the axis x:0 to axis x:1?

Try putting this script under the part.

-- This code make it move from x:0 to x:1 all WHILE going transparent. 
-- Then it repeats all over again from being at its original position and transparent 0

local part = script.Parent

while true do
  part.Transparency = 0
  part.Position = Vector3.new(0, 0, 0)     --Put the desired original position instead
   for i = 0, 1, 0.1 do
     part.Transparency = i
     part.Position = Vector3.new(i, 0, 0)
     wait(0.1)
   end
  wait(1)
end

--This code makes it move from x: 0 to x: 1 BEFORE making it transparent

local part = script.Parent

while true do
  part.Transparency = 0
  part.Position = Vector3.new(0, 0, 0)     --Put the desired original position instead
   for i = 0, 1, 0.1 do
     part.Position = Vector3.new(i, 0, 0)
     wait(0.1)
   end
 part.Transparency = 1
 wait(1)
end