Proper way to enter Mexico

No, you do not need to contact the Mexican consulate or anything else before entering Mexico. I've checked into Mexico many times. I do usually deal with an agent Berto in Cancun. You basically show up with a quarantine flag, fill out all of the appropriate papers (Make sure to have your origional documentation and passports for everyone aboard, and the customs agent or Mexican official will stamp your passports and collect the customs fee.

Apparently some vessels coming down fro San Diego and points north have been refused entry due not having a "zarpe" from their departure port, seems it is a requirement for Mexico though seldom enforced.
I would advise checking with an agent prior to departure.

I have had the same experience many times on both coasts north and south, Makes it easy if you have an agent but not really necessary and generally I have found the officials to be professional and honest. I happily use an agent to speed up the process though in the smaller ports sometimes it is hard to find one.

Yes, you need a departure/Clearance from US. Customs if you are a Foriegn Flagged vessel. As far as I know, this is not necessary for US documented vessels entering Mexico.