So in summary:
"To" is a preposition, like toward or into, e.g., I'm going to the beach; I'm going to the supermarket.
"To" is part of an infinitive verb, e.g. to run, to jump, to go, etc.
"Too" is an adverb describing the degree or extent of something, e.g. too long, too hard, too soft, too hot.
"Too" means "also," e.g., I want cake, too!