Township and range
Each survey area starts from two lines: a principal meridian running north and south, and a baseline running east and west.
Townships are rows counted north or south of the baseline. T2N is the second row north. Ranges are columns counted east or west of the meridian. R3W is the third column west.
The square where a row and a column meet is also called a township. It is nominally six miles on each side.
There are dozens of principal meridians, so a full description names one, for example "T2N, R3W of the 6th P.M."
Sections
Each township is divided into 36 sections. A section is nominally one mile square and 640 acres.
Numbering starts at the northeast corner with Section 1 and runs west along the top row to Section 6. It then drops down a row and runs back east, and continues back and forth until Section 36 in the southeast corner.
Sections along the north and west sides of a township often are not a full 640 acres. Surveyors placed the extra or missing acreage there, in numbered lots.
Aliquot parts
A section is split into halves (320 acres), quarters (160 acres), and quarter-quarters (40 acres). Each smaller piece can be split the same way.
Read the calls from right to left. NE/4 SW/4 means the northeast quarter of the southwest quarter. Find the SW/4 first, then take its NE/4.
Common mistake: N/2 NE/4 is the north half of the NE/4, which is 80 acres. It is not the north half of the section.
A comma separates tracts. "N/2, SE/4" is two pieces: the north half plus the southeast quarter, 480 acres in all.
Put it together
A full description is read from the largest area to the smallest: meridian, then township and range, then section, then the aliquot calls from right to left.
Work through the description on the right one level at a time. The highlighted part is the one to find next.
Descriptions in deeds and leases often run the other way on the page, starting with the smallest call. The order you read them in stays the same.