Indexes to naturalization records are typically found on index cards, as presented in the National Archives and Records Administration files. They vary greatly depending upon which state created the index and what time period the card files reference. Some cards provide a great deal of information while others simply provide a number to look for in the court records.
Most indexes are organized alphabetically, except in the cases where they are in soundex order. Scroll through the image window to see the variety of index cards used and information available. Below are some examples of different types of indexes at Fold3.
A note about New York, Eastern District Court, from NARA's descriptive pamphlet found here:
The index reproduced on this microfilm publication [New York, Eastern District] refers only to those aliens who sought naturalization in the US District Court for the Eastern District of New York, located in Kings County, New York. An alien, however, could become a naturalized citizen through any court of record, making it possible for those living in any of the five counties that made up the eastern district to seek naturalization through the city or county courts in the counties in this district. This index, therefore, does not contain the names of all individuals naturalized in the counties of Kings, Queens, Richmond, Suffolk, and Nassau. The clerks of these county courts will, as a rule, have custody of the naturalization records of aliens who became citizens in their courts.