The instructions for transporting the Ark of the Covenant are detailed in the book of
Numbers in the Bible. Specifically, you can find the relevant information in
Numbers 4.
Within Numbers 4, God gives specific instructions to Moses and Aaron about which Levite clans (the Kohathites, Gershonites, and Merarites) were responsible for transporting different parts of the tabernacle, including the Ark of the Covenant. The Kohathites were specifically tasked with carrying the most holy objects, including the Ark, but were not allowed to touch them directly. They were instructed on how to properly cover the Ark with specific cloths and poles for transport.