Specific standards or test methods from AASHTO published up to 2015 can be found in Standard specifications for transportation materials and methods of sampling and testing, located in Thode Library Bookstacks and Reference (lower level). More recent volumes are available online through the catalogue.
There are four volumes: Part 1: 1A and 1B, and part 2: 2A and 2B.
Parts 1A and 1B contain the specifications. Specifications have designations such as <M29-03> and <R29-02 (2006)>. The numbers <03> and <02> refer to the year the standard was published. Another date in parentheses simply indicates that the standard was re-affirmed in that year.
Parts 2A and 2B contain specific tests. All of these tests have the designation <T> and the number of the test; e.g. <T-21-05> or T319-03 (2007)>. Again, the other numbers refer to the year.
There are indexes in each volume that will tell you which volume contains which standard or test.
AASHTO Provisional Standards contains standards that have not been affirmed and are not in the other volumes. They are listed in alpha-numerical order by subject in the table of contents - check the table of contents if you are searching for a particular number (there are not that many).They have designations such as <MP-16-07>, <TP-61-02> or <PP-34-99>. A <P> denotes a provisional standard.