Do frequency analysis by counting the number of occurrences of each letter.
For a transposition cipher, the counts will be similar to the underlying language (e.g. E T A O N will be common in English).
For a substitution cipher there will be the same distribution of counts as the underlying language, but the high counts will match with the wrong letters.
For Vigenere, the counts will be more uniform and closer to being equal.
If you have matching plaintext, the counts for transposition will be identical; the counts for substitution will be the same numbers in a different order; the counts for Vigenere will be very different.