You need to understand the difference between "to" and "too". "To" is often the first part of an infinitive verb (e.g. "to eat", "to go", etc.); there are several other usages of "to". "Too" is used as an adverb to mean "also", "in addition" or "very."
If someone asks you:
Q: "Do you want to eat?"
A: "Yes, I want to."
While the person will understand your response (oral English), it would be more proper to add the infinitive verb at the end of the sentence - e.g. "Yes, I want to eat."
"I want too." is an incorrect sentence. It can be corrected, however, with a minor change.
If someone asks you:
Q: "I am eating ice cream. Would you like some?"
A: "Yes, I want some, too."
In this above example, the "some" in your answer refers to ice cream. The use of "too" is an example of expressing "also" - i.e. "Yes, I want some [ice cream], also."