Roll out your structural engineering drawings and reference the footing plan. The details will show how deep and how wide your footing excavations need to be. This picture shows a section drawing of a slab foundation with a thickened edge footing, to be technical. As shown, the perimeter footing of this foundation is only 12" x 16". Most pieces of excavating equipment cannot dig a hole this small due to the size of their digging buckets. This footing is perfect for the process shown in the following steps.
Rent an electric breaker hammer with a wide chisel, known as a paddle. The best breaker hammers are made by Hilti and Kango. Contractor rental centers have these on hand and will rent to the general public. They will have various models, so just tell them what you will be doing with it and they will select the proper model for you.
Using your tape measure and white marking paint, measure and mark the basic layout of the foundation. Be sure the corners are easily identifiable.
Layout your footings with a string line and stakes. This process will enable you to create straight lines and square corners. Hammer three stakes into the ground about 3'-0" past the corner markers of the foundation. Each stake should be about 3'-0" away from the other creating a square corner. Screw a 1x4 piece of wood across the stakes, this is your batter board. Importantly, the batter boards don't need to be totally square themselves. The string line is the only component that is required to be square.
Prior to pulling the string lines, make sure your batter boards are level. Use a basic level, check the boards and adjust as necessary. Now, following the outside line of the foundation back to the batter board, tack a nail into the top of the batter board marking that line. Do this for both walls that create your corner. Pull your string lines in between all points.
Square up the lines using one of two proven formulas. First is the Hypotenuse Rule or 3-4-5 check, which states the hypotenuse should be 10'-0" when one leg is 6'-0" and one leg is 8'-0". Just measure back from one corner 6'-0" and mark the string, then measure the opposite string back 8'-0" and mark it. Finally, measure the diagonal between those two marks to the hypotenuse. You can also use the Diagonal Method in which you measure both diagonals as pictured and adjust your strings until both diagonals are exactly equal.
Now, tie a plumb bob to the intersecting strings at your foundation corners. The plumb bob should rest just above grade. When the plumb bob is resting at plumb, drive a nail into the grade at that point. Do this on all corners and then pull a string line right on top of the grade between these points. When finished, spray marking paint directly over this string line. Go over the string accurately and repeatedly for a nice, clearly visible white line on the grade.
Remove both the string line at grade and the string line tied to the batter boards. With those out of the way, you can begin the excavation process. Cut your footing against the painted line at first. Continuously shovel your excavated soil to the outside of the foundation area. You don't want to cross over excavated footings with a wheel barrow or other equipment, it will just cause you more digging and headaches.
Call a local debris box company and have them drop a dirt box in the front of your house or driveway. You can build a ramp and run the wheel barrow right into it to dump your excavated soils. When it begins to get full, you will have to start filling 5 gallon buckets, wheeling those out and dumping them by hand. Don't worry about using the buckets, I have excavated entire house foundations and removed the dirt with buckets due to hillside conditions and other limitations.