When do you use "into" vs "in to"?

Hello, and thank you for your excellent question!
While both 'to' and 'into' are prepositions they are used differently:
The preposition 'to' is used to talk about action, motion and direction. We use it to show movement from one location to another - 'I walked to the park' - in other words you walked from one place and you are now at the park. But, are you necessarily inside the park? No, and that is where the word 'into' comes in.
The word 'into' is used to show movement that results in being enclosed by something - 'I walked into the park' - you are now inside the park and enclosed by it. 

I hope that this explanation and these examples help you!