This is in Texas County, Missouri. The sections along the
northernmost tier of T 29 N are all about a mile wide by around two and
one half miles tall. Here's how this is handled.

The southernmost Quarter Sections, the SW and the SE are of about normal
size. the remaining two miles is divided up into eight "lots" of about 80
acres each or about a Half-Quarter Section.
Quite often, a property description will describe an
otherwise square tract which is bounded on one or more sides by a road or
stream. In this case, a property that looks like this:

Will be described as "All that part of the West Half of
the Southwest Quarter of Section 15 lying south of Coatney Branch and
North of Highway 73..."
There are other systems of survey description most notably "Metes and
bounds", which describes distances (metes) between different monuments
(bounds). While this method began with descriptions like,
"Begin at the stone outcropping on the Elisha Wilson farm, thence proceed
15 rods north to a large hickory tree". The original thirteen
American colonies as well as Kentucky, Tennessee, parts of Ohio, Maine and
Vermont were divided using this method. Here's a modern example
which makes reference to the Government Township and Range.:
Now I'd like to end up by
saying something like, "and that's all there is to it".
Unfortunately, that's only the beginning, but this will get you started
and you'll be able to talk to your county recorder without looking too
silly.
You'll also need to
be familiar with a few terms of measurement that I've included below:
Linear Measure:
1 link = 7.92 inches
1 rod = 25 links = 16.5 feet
1 chain = 4 rods = 66 feet
1 furlong = 10 chains = 40 rods = 660 feet
1 mile = 8 furlongs = 80 chains = 320 rods = 5,280 feet
Square Measure:
1 square rod = 272¼ square feet (30¼ square yards)
1 square chain = 4,356 square feet
1 acre = 43,560 square feet
1 square mile =
640 acres (one section)
1 township x 1 range = 36 square miles