Along with looking at the frequencies of letters, it is often helpful to consider how letters relate to one another. You can often tell which ones are vowels because vowels are "friendly," that is, most letters appear before and/or after them. Thus, if there is a letter in your ciphertext that appears in pairs with many different letters, it may be a vowel. To find out which one it is, remember that 'a' is almost never doubled, 'e' is incredibly frequent, and 'u' is relatively rare.
Another helpful trick is to consider
digraphs, that is,
pairs of letters. The digraphs also follow frequency patterns,
so finding out which of your digraphs is most frequent will often
reveal information about your ciphertext (see the
digraph frequency table).
To count the digraphs, it's helpful to make a 26x26
table, with all of the letters labeling each row and column. Then, if you see the pair "VQ", put a hash mark in the space on row "V" column "Q". Obviously, this takes some work, but if you work as a team it can be done quickly!