The first standardized public land surveys in the United States were made in Ohio in 1786 under an ordinance of the Continental Congress passed May 20, 1785. Though modified since its adoption, the act is still the basis for all surveys of United States public lands, except private land grants.
Briefly, this system is as follows:

Base Line and Principal Meridian
The first step in putting this survey system into operation in a given area is the establishment of an "initial point." This point will be the basis for all government surveys in the area it controls, and its latitude and longitude are fixed by astronomical observations. From this point, a Principal Meridian is run north and south on a line that would interest the poles, and a Base Line is run east and west on a parallel of latitude. The principal meridians are given name or number designation for use in describing land.

Standard Parallels and Guide Meridians
Because of the curvature of the earth, additional lines called Guide Meridians are run every 24 miles east and west of the Principal Meridian, Other lines, called Standard Parallels, are run every 24 miles north and south of the Base Line. The Parallels north of the Base Line are designated First Standard Parallel North, Second Standard Parallel , etc., and those south as First Standard Parallel South, etc. These Guide Meridians and Standard Parallels also are know as Correction Lines.

Ranges and Townships
Lines next are run North on true meridian from Standard Parallel and 6 miles apart, thus marking the surveyed area into strips 6 miles wide called Ranges, which are numbered East and West from the Principal Meridian. Similar lines are run at every 6-mile point North and South of the Base line, and parallel with the Base line, cutting the Ranges into squares, 6 miles each way, which are called Townships.
The first Township North of the Base line is numbered Township 1 North, the second Township 2 North, etc. Those South of the Base line are numbered Township 1 South, Township 1 South, etc.

Sections (see sectional map below)
Townships are subdivided into 36 parts-each one mile square, as near as may be, called Sections-accomplished by running through the Township, each way, lines parallel to the South and East Township boundaries at the end of each mile. The interior meridianal or North and South Section lines therefore are intended to be straight lines ordinarily for 1 mile only, parallel to the East line of the Township, except those next to the North line of the Township and the interior latitudinal; East and West Section lines are intended to be straight lines for 1 mile only, parallel to the South line of the Section. The 36 Sections into which the Township is divided are numbered from 1 to 36 beginning with the Northeast corner and proceeding West and East alternately through the Township.
The Sections are the smallest tracts the law requires to be surveyed but further subdivisions are made by the division of the Sections into 4 quarters containing 160 acres more or less, and named Northeast Quarter, Northwest Quarter, Southeast Quarter and Southwest Quarter. Due to the earth curvature and unavoidable errors, the Sections along the North Boundary and West  Boundary of each Township are irregular. The quarter sections along the North and West boundaries of these sections take up the excess or shortage in the Township, and the Quarter Quarters along the North and West Township boundaries are given Lot Numbers; for example, Lot 2, Section 5, Township 42 North, Range 12 East, or Lot 7, Section 31, Township 41 North, Range 9 East.
In several states, a Township frequently will be occupied partially by Indian lands.  United States Government Surveys did not cover these lands, and an intersection with the boundaries of them resulted in fractional Townships.
Fractional Quarter Quarters in the Sections created by reason of the Indian lands are given numbers by the Government at the time of survey; for example, Lot 2, Section 26, Township 40 North, Range 9 East. Also, when the meander line of a body of water is a boundary or when there is an excess or deficiency due to natural error in a section or township, the Fractional Quarter Quarters thus created are described as Section Lots. In short, a Lot exists for the purpose of describing sectional property which cannot be described as a true Quarter Quarter or 40 acres.

Some samples below: