Much of New Mexico is subdivided into a grid, the Public Land Survey System (PLSS) based on townships and ranges. The PLSS is a roughly gridded network of surveyed lines and monuments; approximate 6-mile by 6-mile "townships" composed of approximate 1-mile by 1-mile "sections.
Some parcels of land are not subdivided, particularly in the northern and central parts of the state. Most of these areas are either tribal lands or are parts of old Spanish land grants.
In New Mexico, townships are numbered either north or south of a central dividing line, while ranges are numbered east or west of a central dividing line. To completely describe a township, you would use both the township and range (eg., the township to the left is T1N R3W).
Go to http://daihatsu.nmt.edu/waterquality/maps/PLSS.html to see county maps for the state showing townships and ranges.
A typical section of land in New Mexico contains 640 acres. A half-section would be 320 acres (1), a quarter section would be 160 acres (2).
A normal section would be divided into 16 forty-acre tracts.
At left is a normal section of land with 16 identical forty-acre tracts, or quarter-quarters. In a normal section of land, the tracts are designated alphabetically starting with the northeast quyrater of the northeast quarter as "A" and zig-zagging through the section to "P".
If the section is significantly longer, extra lots are designated at the north end in sig-sag fashion; same with the west side if the section is significantly wider.
A rule of thumb...the portion of the section that ALMOST remains unchanged regardless of geometric fluctation is the southeast of the southeast corner, or quarter-quarter.
A last note - there are rare sections within New Mexico which defy any sort of configuration convention; consult title surveys for those.