This adds significant strength to the encryption when compared with monographic substitution ciphers which operate on single characters.
The frequency analysis of digraphs is possible, but considerably more difficult - and it generally requires a much larger ciphertext in order to be useful.
The key can be written in the top rows of the table, from left to right, or in some other pattern, such as a spiral beginning in the upper-left-hand corner and ending in the center.
When only the ciphertext is known, brute force cryptanalysis of the cipher involves searching through the key space for matches between the frequency of occurrence of digrams (pairs of letters) and the known frequency of occurrence of digrams in the assumed language of the original message.
Cryptanalysis of four-square generally involves pattern matching on repeated monographs.
For instance, the word MI LI TA RY will always produce the same ciphertext letter in the first and third positions regardless of the keywords used.
A good tutorial on reconstructing the key for a four-square cipher can be found in chapter 7, "Solution to Polygraphic Substitution Systems," of Field Manual 34-40-2, produced by the United States Army.