Upon arrival at the International Puerto Vallarta Airport you'll first go through immigration, then you'll pick up your luggage on the carrousels and then you'll go into the customs area where you will be asked to push a button that will randomly determine if your baggage will be checked or not (though at some point it was mentioned that it wouldn't be used any more, it's still in use).
If you get a green light you are free to continue to the exit gate through the so-called shark tank (timeshare people, read more), if you get a red light you will need to take your bags to the customs counter and have them checked.
This system is totally random and tends to show many more green lights than red lights.
More on the duty-free - tax-free allowance section.
Please check at the Mexican consulate in your city for necessary documents to come to Mexico, or even easier, visit the US Travel Gov site for more information.