uses of onto and into

Plainly, "into" is a combination of "in" and "to" (though it's no more written as two words, "in to") while "onto" is of "on" and "to," and some people want to split it down to its two components--"on" and "to."

The "to" part of these two prepisitions indicates a movement toward a point given by the noun phrase (NP) following it. The "in" and "on" parts describe the spatial/dimentional relationship between what moves and the space/point given by the NP following the prepisition.

Let's consider the following examples.

1. She moved the books onto another shelf.
2. He goes into the garage.

In (1), she changes the place of the books "to" a new place, that is, another shelf. When the books are at this new place, they are "on" the another shelf. Thus, she has moved the books "to" and "on" another shelf; that is to say "onto" another shelf.

In (2), he moves and reaches a new point. It is like this: He moves from point A "to" pont B. He was somewhere else, but now he moves "to" the garage. In his kind of movement, he does not stop "near" or "outside" the garage. He does not stop "at" the door of the garage or "behind" it either. Once he completes the action (that is "going"), he is "in" the garage, the building, the structure. The goes "to" the garage and this action puts him "in" the garage. So, you simply say "He goes into the garage."

This explanation has considered only the basic, literal senses of "into" and "onto." If you want to know more, my first best recommendation would be a good dictionary, such as Oxford Advanced Learner's Dictionary.