An infield is simple geometry.
Using apex of the 90° angle on the home plate, you will want to
set up a transit. You can usually rent one from a local surveyors supply.
Every groundskeeper should own one. You can buy a relatively inexpensive
transit for about $300 to $400 with a tripod and an elevation rod (which
you need for establishing the height of the pitchers mound).
You will need to set the transit up so that a plumb bob, when hung from
the hook under the transit, lands directly on the apex of home plate. Then,
you level the transit using the leveling bubble on top. Once this is done,
turn the optics and locate the right field foul pole.
You will want to pull a string line to set your first base line. There
is a 360° dial on the base of the transit. Turn that dial to zero
and lock it down.
Next, knowing that the field is a square, making the angle to third base
a 90° angle, turn the optics to the 90 marked on the dial. This
should aim the optics directly at the left field foul pole. If it does
line up, great!
If it doesn't line up, that means home plate isn't where it is supposed
to be. You will need to figure out where it should be based on where the
optics are landing in relationship to the left field foul pole. If it
is easier, you can even move the foul pole to make it work. Pull another
string line for the third base foul line.
Now that you have your foul lines established, measure out to whatever
base distance you are working with to set the First and third bases.
Then you will pull a tape from the First base and third base. Where those
two tapes come together ( at whatever base distance you are using) that
will be the center of second base.
Your field is now squared up.
To check yourself, turn the optics of the transit back to 45°.
You should be able to see the intersect point of the two tapes.
If you want to do it the hard way, you can use the 3-4-5 method. Start
at the apex with a string line pulled all the way to the right field foul
pole. Pull a string line out from the apex to the left field foul pole
area. Then measure 3 ft. up the First base line. Measure 4 ft.up the third
base string line. Measuring from those points, swing the third base line
string until you get exactly 5 ft. from point to point. This method isn't
nearly as accurate, but will still work.
This is a very long-winded method, but there just isn't a quick and easy
way to do it otherwise.
