Through the use of a rectangular, or Cartesian Coordinate system we are able to preserve the site on paper and accurately record all the relative data. Another benefit of doing this is that future researchers can return at a later date and better visualize details from the notes taken at the time. Any evidence collected is much more reliable when every step of it's collection process is accurately recorded, the more stringently the better.
The first thing to consider is the scale that you need to use...obviously if you have a three hundred square foot area to investigate, you don't want to set up a one foot by one foot grid system on the ground. It would be much more practical in this instance to set up a grid system whereby one inch on paper equals ten feet on the ground. This is the scale model that we will use for this example.
After deciding your scale, you will want to set your first site datum point by picking an arbitrary location to place a stake, and then designate that point as (0,0) both on your diagram on paper, and with tape or marker on your stake. At this point I personally like to use both my compass, and my Theodolite App to get my grid aligned to a North-South axis. Then I get my bright orange waxed string out and tie it to the stake at (0,0), attach my tape measure to the stake, then walk South the desired distance of the size grid being used, and place another stake so that it is both the correct distance, and the string is aligned perfectly with the North-South axis. This stake should be numbered in the same manner, using (0,?) and whatever unit you are using in your grid. For our example we'll go with ten, so it would look like (0,10).
Next return to datum point (0,0) and repeat the process, except in the easterly direction, and the end datum point for that line will be (10,0). I also like to check that line with a square for accuracy. Once this outside framework is established, it is a simple matter to measure out the rest of the grid by following each axis 1-9 with the orange waxed string and placing a stake with a marker in each grid corner that gives each point a unique name...such as (3,7). With that coordinate location a person can later come back to the diagram and know the exact location being referenced. Once the grid is in place, any artifacts found that were visible on the surface can be collected, and their locations recorded on the grid.
There are many different types of grids, with many applications. There are spiral grids, three dimensional grids, circular grids, and certainly some I don't know about (I'd be surprised if there wasn't!), and many different ways to graph your grid as well, especially if you are any good at 3D modeling. Hopefully this will give you a head-start on learning how to set one up without having to take a refresher course in geometry!