Hook into form submission

Hi, I am a seasoned coder but I am not very knowledgeable when it comes to wordpress. I need a very simple way to hook into the form submission.

I need to have access to all fields to prevent the submission in certain situations. The logic will be very specific so no available plugin will be helpful.

So can I just add a hook with a callback to my theme or something?

To be clear: I just need help with:
* where to put the hook callback
* how to access the submitted fields within the callback
* how to actually prevent the submission within the callback

Thanks!