The national code for residential concrete foundation construction is the American Concrete Institute Manual 332. It contains all the needed information for building a foundation correctly.
The most important item in building a foundation is the neccessary weight load transfer to the dirt. Once the weight of the structure and the substrata's load bearing capacity is known, you can determine the needed width of the footer.
Changes occurring in any dirt are associated with moisture. In Texas foundations are not affected by freeze but by the summer drought, followed by the over abundant fall/winter/spring rains. So while the northern half of our country has what is called a frost line, Texas has a "drought line." Any foundation in Texas, regardless of type, must be built below this depth to be successful. In Texas, the average seasonable moisture change damageable depth is approximately 36 inches.
Footers are the first part of any construction. The purpose of a footer is to transfer the weight-load of the home to the dirt. It's width is determined by the weight of the structure and the bearing strength of the substrata. Wider is always better than narrow. Typically a 24" wide footer will handle most residential projects. To combat the movement of the earth (known as a drought line in Texas) a depth of three feet is recommended
The walls are the second phase in basement construction. There is a difference between a structural wall and a retaining wall. A structural basement wall has constraint at the top which is provided by the floor system's lateral support. It is this lateral support that makes it different from a retaining wall.
The basement floor is the final pouring stage of basement construction and yes, even a slab foundation can be built to resist soil movement and provide the appropriate strength for a structure if all factors are understood and accounted for. The basement floor is a non-structural component of the basement, meaning the floor is a walking surface only.