The pairs into/into andonto/onto cause a lot of confusion for writers, but much of that confusion can be cleared up if you focus on exactly what you are trying to say.
A. IN TO vs. INTO:
I. Into is a preposition. In a sentence, the preposition into will be part of a prepositional phrase consisting of into + its object + any modifiers of its objects. The entire phrase it is a part of will function adverbially to modify the verb or verb phrase that precedes the phrase.
1. When he walked into the room, he found that the meeting had already started.
2. Put the toysinto the basket.
3. The pumpkin was turned intoa carriage.
II. In the phrase in to, in is an adverb, directly modifying a verb, and to is a preposition with its own object. When the word into is used in a sentence where in to is meant, the resulting statement can be absurd.
1. She turned her paperin to the teacher.
2. She turned her paperintothe teacher.
In the second sentence, the paper is transformed--poof!--into the teacher. We've all heard the old joke about the magician who was so talented that he could drive down the street and turn into a gas station. Of course, if he just wanted to get gas somewhere, he would turn in to a gas station.
1. Put the cookie back into the jar.
2. I need to turn this book backin to the library.
3. Would you hand this assignment in to the teacher for me?
4. Turn your badge in to the officer at the desk.
5. Cinderella stepped into the carriage.
6. At midnight, the carriage turned back into a pumpkin.
B. ONTO vs. ON TO:
I. This pair works pretty much the same way the into/in to pair does, except that there are a number of sentences where either form would be correct, depending on the intended meaning. Take a look at some examples:
1. The responsibility fell onto his shoulders.
2. She tossed the book onto the desk.
3. We drove onto the turnpike. (We got on the turnpike.)
4. We drove on to the turnpike. (We drove until we got to the turnpike.
5. The restaurant adds the tip onto the bill.
6. Please pass this information on toyour clients.
7. It would be more profitable to shift the cost onto your customers.
8. It would be more profitable to pass the coston to your customers.
II. I actually believe that studying pairs #3 and #4 and #7 and #8 will tell you more about when to choose onto and when to choose on to than a lot of explanation involving grammatical terminology.
Just remember, the two expressions do not mean the same thing, so make sure you know exactly what you are trying to say, and then you will be likely to choose the right word or phrase.