How to find key length of a Vigenere chiper?
First find repeating substrings, longer repeating substrings are better. Look at the differences between the index of repeating subsring pairs. Calculate GCD of the differences.  If it is a reasonable key length you probably have it. If it came out 1 try dropping some outlier spurious substring occurences. If it came out too large to be a reasonable key you may need to find more repeating substrings allow shorter substrings to be considered. 

Motivation:
We expect many repeating substrings of common char-grams, in English for instance : th,the,ing and more if these appear in a difference which is a multiple of the key length the cipher text fragments will be identical as well. However such a repeating cipher text is unlikely to appear from encripting some other text in another column.