There is not any common algorithm, that would be used in all transposition ciphers. The main idea is to change the letter order in such a way, that would prevent attackers from reading it, while at the same time, allow the receiver to decrypt messages easily and effectively.
Both sender and receiver should share a common secret, usually a keyword, that determines the exact transpositions that should be applied to the text.
Transposition ciphers usually require more memory and more complex operations, than substitution ciphers. That is why modern ciphers implemented pragmatically and electronically are usually based on substitutions, and less often on transpositions.