A trade machine is used to trade Pokémon with other players. It has no real use in singleplayer.
Trade machines can be obtained by crafting them. A pickaxe is required to retrieve them once they are placed. When crafted, there is a small chance that you will receive one of Porygon's constituent parts, used to create the Porygon item.
It is possible to use dye on a trade machine to change its color. This cannot be done via the crafting interface; the trade machine must first be placed. Only the player who placed a trade machine may dye it. After dyeing a trade machine, breaking it will still return the default red trade machine as an item.