Theistic evolution has been variously defined as the belief that God created all forms of life gradually over a course of millions of years, just as mainstream geology and paleontology says, but by intervening directly to create each major type (see Old earth creationism; or the belief that evolution by natural selection was the indirect means by which God created the variety of life.
Note that these two definitions contradict each other. Old Earth Creationists maintain that it was only by God's direct intervention that the various forms of life came into being. They deny the theory of evolution, on the grounds that natural selection is not a sufficient creative force, or on Biblical grounds; or on both grounds taken together.
There is considerable disagreement over how many people (in America) are theistic evolutionists. Much of the disagreement stems from disputes over the meaning of the term. These disputes are generally related to debates over how many people "believe in evolution".
If "belief in evolution" means accepting a natural process which occurs without God's intervention, then only a minority of Americans accepts this (around 12% to 18%, depending on polls). But if it means accepting that some aspects of evolution have occurred - such as the gradual appearance of the various species - then actually a majority of Americans belief this. This includes the believers in a natural process alone, combined with the Young earth creationists who say life emerged gradually but by God's direct intervention.