On Cinco de Mayo in the few southern states that I have seen it celebrated, the beverage of choice is a margarita. An yes Eliza you were correct about the salt around the rim.

Tequila shots as gnu described are limited to "frat boy" types who like to drink in a showy manner.

My favorite way to take tequila is to sip a high quality brand such as Patron from a shot glass. But that is a very expensive way to drink.