Correspond with someone/something:
* Means to communicate with someone.
* Example: "I correspond with my pen pal regularly."
Correspond to something:
* Means to be similar or equivalent to something else.
* Example: "The information in this report corresponds to the data we collected."
* Can also mean to match or fit.
* Example: "This key corresponds to this lock."
In short:
* Use "correspond with" when talking about communication.
* Use "correspond to" when talking about similarity, equivalence, or matching.
Let me know if you have a specific sentence in mind and I can help you figure out the correct preposition!