The Shulhan Aruch prohibits covering a large barrel whose contents are not filled to the top with a cloth on Shabbat. Doing so constitutes making an Ohel (tent), since the cloth is an overhanging, and the sides of the pots are the walls. Based on this, the Poskim discuss whether it is permitted to cover a pot with aluminum foil or plastic wrap. Ostensibly, this should also constitute making an Ohel. Nevertheless, the Poskim are generally lenient, since the walls of the pot need no assembly; they are already in place. In such a case, there is no problem of Ohel. Covering a pot with its cover is certainly not a problem, because that is the normal way to use the pot.
One might argue that this leniency only applies when the pot remains in one place, but if the pot is moved, it should be prohibited to cover it, since moving the pot is tantamount to reassembling the walls. This argument is based on the ruling of the Mishna Berura (Rav Yisrael Meir Kagan, 1839-1933) in Siman 315:22, that although it is permissible to put a board across two pre-standing barrels, nevertheless it is prohibited to move the barrels and then lay the board across.
The Poskim reject this comparison between the pot and the barrels, based on the argument of the Hazon Ish (Rav Abraham Yeshaya Karelitz, 1878-1953 in Siman 52:10). The pot remains intact before, during and after it is moved. The walls of the pot remain suitable to be covered even while being transported. On the other hand, the case of the table is different, since while the barrels are being moved, the entire frame of the table is broken; one could not lay the tabletop while the barrels are being moved. Therefore, the barrels in the new location are considered reassembled and laying the tabletop is a problem of Ohel.
It is permitted to cover a pot with foil or plastic wrap on Shabbat.