There are many different foundation options, each with its own advantages and disadvantages. If you are building on ground that has a low bearing capacity --- such as very soft and silty soil --- you will probably find that a raft foundation is the preferable solution. A raft foundation spreads the load of the building across the entire area of the building, as the foundation itself extends underneath the entire floor --- like a 'raft' for the structure.
Mark out the area of your foundation using pegs and string. You may need the services of an engineer to do this accurately.
Use the excavator to remove a layer of soil to a depth previously stipulated by the architect or engineer. Use the compactor to form a hard surface once excavation is complete. Excavate to a greater depth where your external walls are located, as these areas will carry a greater load.
Use a crane to lower the metal pan into the excavated area, or do it by hand if you have enough help. Lay the reinforced mesh in the pan, slightly elevating it using small metal "chairs" at regular intervals.
Pour the concrete into the pan and tamp it down with a piece of wood. This is where one person on either end of the wood strikes the surface together in order to remove bubbles of trapped air and give a smooth finish. Also pour concrete into the deeper areas where your external walls will be built, reinforcing the trench once again with mesh.
Wait for 48 hours for the concrete to cure.
Make sure a qualified engineer calculates the correct depth before you begin.