The first thing you have to do is dig an area out that is below the frostline for your footing to sit on. You should then grade it level and compact it with a plate compactor or "jumping jack", which can be rented for around $25-$40 per day.
A typical footing for a 2 story home is 16"-24" wide and 8" deep, which depends on the thickness of your stem wall which is typically 8" thick. If you have anything less than 8" I've found that it will tend to crack quite a bit. Figuring the size of your footing is pretty easy; take the thickness of your stem wall and that will be the depth of your footing. Now take half the thickness of your stemwall and this will be how much to extend past the sides of your stem wall. So adding these up we get 4" to each side of the stem wall and the width of the stem wall equals 16".

Forming the concrete footing is typically done with 2x8's, which are only 7.25" wide. This is not a problem, because I usually want it a little above the ground to enable me to easily level the top of the formwork without having to dig after I have compacted the area.
You will now need a 5 lb hammer or maul to drive the form stakes around the outside of the formwork. I usually get the outside form put together first and stake one corner solid. Then working from that corner I will "square it up". Stake the other corners after you have it squared. Then I will run a stringline from corner to corner, pulling it very tight, and line the formwork to the stringline and putting a stake approximately every 4'. Now I will nail the inside form together, and place rebar into the footing.
Rebar in a footing will give it added strength, so don't leave it out. I use 2 - #4 bars continuous around the middle of the footing. Place the rebar approximately 6" in from each edge of the formwork. Later we will tie the rebar to the "spreaders" so it will be in the middle of the footing when we pour concrete.
The spreaders, made from 1x4's, will hold the formwork at the correct distance apart. The spreaders should be 3" longer than what your finished width of the footer is; so a 16" footing will necessitate 19" spreaders. This makes it easy to install the spreaders by lining up the ends of the spreader with the outside edges of the formwork and nailing it. I put my spreaders between the stakes that we put around the outside edge of the formwork. Now your inside dimension of the formwork should be 16" or pretty close anyway. I will then drive more stakes around the inside piece of formwork at 4' apart, and leveling across with a 24" level from the opposite side stake which has already been leveled. We will check these elevations again before we pour the concrete. Take some of the dirt from your excavation and place at the base of your formwork around the whole outside, this will lessen the amount of concrete that will run under your formwork and provide more support so the formwork doesn't bend. As stated earlier, now is the time to tie the rebar up into the middle of the formwork.
Approximately 6" in from each edge of the formwork take some tie-wire and run under the rebar and up over the spreaders (one piece of rebar at a time), pull the rebar up until it is in the middle of the formwork and twist the tie-wire to hold it. Remember to overlap each piece of rebar with the next piece in line by about 6" minimum, or 12 times the diameter of the bar, and tie wire 2 times at each splice. Complete the rest of the rebar the same way. After you pour the concrete you will need more rebar to place in the top of the footer to "connect" the footer and the stem wall, cut them now so you're ready. They should be the same height as your stem wall so when we place them in the footer 6" they will be 6" from the top of the stem wall and not interfere with anchor bolts or any embed plates.

You are now ready to pour the concrete into your formwork. To figure how much concrete to order you can use the Foundation Calculator on this site or do it by hand. When doing it by hand you multiply the width by the height and then by the length of the footing (use measurements of feet, so 8" would be .666 feet). This will give you cubic feet, but we need cubic yards; so divide the number by 27, which is the amount of cubic feet in a cubic yard. This number is called a neatline quantity, but we all know that formwork is not neat. We will want to add a factor of waste into this so we don't come up short in our pour. Typically the factor of waste for pouring against the ground is 12% and pouring against formwork (stem wall) is 8%. Our footing is in contact with the ground so we will take a final cubic yardage and multiply by 1.12 to get our final order quantity.

Pouring the concrete is the final step in the process of creating a footing. Some poeple hate pouring concrete, but I think it's pretty fun. It is hard work though, so have plenty of water on hand. When pouring the concrete into the footing, don't put too much in one spot, try to keep it even throughout the pour. After you have some poured have one person go back and start "screeding" the concrete. You can do this with a 24" length of 2x4. Place it on each side of the formwork and move it back and forth, perpendicular to the formwork, and pull it parallel to the formwork at the same time. This will start the process of getting alot of the air out of the concrete, which will weaken it. You should also tap on the sides of the formwork as you go to further remove air entrapped in the concrete. When you are done screeding you should have concrete that looks like icing on a cake after you run a knife over it. Not perfectly smooth, but flat. Many people won't trowel a footing, because they think it's wasting time. It may waste some time but it makes it a lot nicer later on when we go to put our stem wall formwork together. Troweling a footing is quick; just run the trowel over it a couple of times on the outside 6" to where it is smooth, not perfect. Now you're complete with your concrete pour.

Some structural plans will require a keyway between the footing and stemwall. This is easily created by taking a 2x4 on edge and "screeding" in a 2" deep keyway into the top of the footing. This will give a much stronger connection between the footing and stemwall to help with larger shear values across the footing. In the next step of placing the vertical rebar into the footing you can place them right in the middle of the keyway.

The lengths of rebar you cut earlier now need to be placed in the center of the footing, or what will eventually be the center of your stem wall. When putting this rebar in don't "stab" it in, move it up and down so it will consolidate around the rebar. If you stab it in you will end up with voids around the rebar and it will be loose when the concrete sets up, which doesn't do any good. Place these at around 4' apart with one about 6"-12" from each corner.

The next day you should remove the spreaders and get ready to start placing your formwork for your stemwall. Some people also remove the formwork from around the stemwall, but I like to keep it there until after the stemwall is complete. This allows you to nail a 2x6 into the 2x8 formwork to hold it in place instead of trying to nail into concrete.

Any further questions can be directed to the Forum.