The pamphlet from NARA explains the Soundex system:

The Soundex is a coded surname (last name) index based on the way a surname sounds rather than by the way it is spelled. Surnames that sound the same, but are spelled differently, like BROWN and BROWNE, are filed under the same code. The Soundex coding system was developed so that you can find a surname even though it may have been recorded under various spellings.

To search for a particular surname, you must first work out its code. Every Soundex code consists of a letter and three numbers. The letter is always the first letter of the surname. The numbers are assigned to the remaining letters of the surname according to the Soundex Guide.

NARA Census Soundex (2002).

Follow these simple steps to get the soundex code for any surname.

SOUNDEX CODING STEPS
Step	Process	Example: WILLIAMSON
1.	Write out your surname, cross out any vowels (A,E,I,O,U) and the letters H and W	WILLIAMSON becomes W LL  MS N
2.	Cross out the 2nd of any double letters.	W L   MS N
3.	Cross out any remaining letters after 4 letters (including first letter).	W L   MS
4.	Assign the following codes to the remaining letters. Replace the letters B, P, F, V with the number 1 Replace the letters C, S, K, G, J, Q, X, Z with the number 2 Replace the letters D, T with the number 3 Replace the letter L with the number 4 Replace the letters M, N with the number 5 Replace the letter R with the number 6	W + L=4 + M=5 + S=2
5.	If the surname had less than three letters left, assign zeros to those places.
	Your final code should be the first letter of the surname plus three numbers.	WILLIAMSON = W452

W452 is the Soundex code for Williamson and the following surnames: Walling, Wallingford, Walmsley, Welling, Wellington, Whillians, Willems, Willemssen, Willens, Williams, Willihnganz, Willingham, and Woolums.