It depends on how busy the airport is when you land, and how many booths they have open. You enter the immigration booths one at a time to have your passport checked (obviously one of you can take the baby with you), the door to exit is locked until the guy is happy with you and your passport, and then he unlocks it. I, along with the vast majority of people, have never been asked to show proof of insurance, but make sure you have a copy of it with you. I put mine with my passport, just in case.

Departing is as SMa says. You check in, and then take your passport and boarding card to the booth where you pay your exit tax. Make sure you have the correct amount each in CUC's. They don't give change. How long it takes depends again on how busy the airport is, and whereabouts in the queue for checking in you are.

If you buy entry to the VIP lounge (25 CUCs per person) , you also get separate check in and fast track to pay the exit tax.