Cinco de Mayo is an annual celebration commemorating the victory of the Mexican Army over the French Empire at the Battle of Puebla in 1862. While the official national day is Mexican Independence Day on 18 September, Cinco de Mayo is still a significant date in Mexican history, with parades and celebrations. In Puebla, where the battle took place, it's particularly momentous.
Here's how your own celebratory feast can play out:
Kick off with some appetisers
Get these right, and it doesn't matter what you serve after that, you've won over your guests. Tender poblano chillies (you could also use other small peppers, but poblanos have an appealing gentle heat) filled with cheese, dipped in a light batter, and deep-fried until crisp and golden. They hail from Puebla too, so are a fitting way to get the party started.

Stuffed poblano chillies (chiles rellenos). Source: Sharyn Cairns
Ceviche is simple in terms of ingredients and preparation, so its success relies heavily on the quality of the ingredients: use only fish purchased that day, fresh lime juice, and the best avocados, tomatoes, coriander and red onion you can get your hands on. Serve with crunchy tostadas or corn chips for easy scooping.

Lime-cured fish with avocado (ceviche con aguacate).
Cemitas are like a Mexican hamburger, made on a brioche-like cemita bun that comes from Puebla. Make them slider-size, as part of a bigger banquet, or regular-size, served by themselves with some other appetisers, drinks and a dessert.
Roll out some fresh tortillas

Milanese chicken cemitas (cemitas Milanesas de pollo). Source: Chris Chen
Tortillas are an essential part of any Mexican meal—not even just a feast, any regular meal. The average Mexican eats approximately 250gm of tortillas per day. Compared with wheat tortillas, corn tortillas are a little earthier in flavour and grainer in texture. You'll need a tortilla press to make them—as they don't have any gluten (good for your gluten-free guests), they can be tricky to try and roll with a rolling pin.

Corn tortillas. Source: The Dallas Morning News
Flour tortillas are a lighter and more neutral-tasting tortilla, and a little more forgiving to make; you won't need a tortilla press, but you will need a rolling pin, bottle of wine, or similar-shaped device—and ideally, a kitchenhand!
Dish up some salsas

Flour tortillas. Source: Benito Martin
Tomatillo salsa can be made of raw or roasted tomatillos, depending on what kind of flavour you want to add to balance out your other dishes. This one is fresh and light, but with some smoky depth. Tomatillos are becoming more widely available in Austalia at greengrocers and farmers markets, and can be grown in home gardens quite successfully, where they come into fruit during summer.

Roasted tomatillo salsa.
Don't let looks deceive: the sauce packs a hot punch.
Preserve some pickles

Mango habanero hot sauce. Source: Pati's Mexican Table
Make a bigger batch of these pickles than you think is necessary—they’ll be popular at your Cinco de Mayo banquet, and you then can use the leftovers with everything from sandwiches to burgers and fresh seafood.

Yucatan pickles. Source: Hardie Grant Books
Pickles are a necessary accompaniment for Mexican food, with the sweet and sour flavours cutting through the rich and complex flavours. In this recipe, the ingredients are sauteed first in oil (the "escabeche" element), before being dredged in the pickling mixture.
Serve up a shareable meat dish

Pickled Jalapeño chillies (jalapeños en escabeche).
Mole poblano is the dish of Puebla, believed to have been the creation of 17th-century nuns. It's typically used with turkey or chicken meat, is deep-red in colour, and has sweet, smoky, raisin and cocoa-like flavours from the pasilla (or ancho) chillies.

Mole poblano. Source: Feast Magazine
Pepián sauce is sweet, nutty and aromatic with a touch of heat, and works well also with chicken and prawns.

Pumpkin seed sauce with poached pork (pepián con cerdo).
As luxurious-tasting as it is luxurious-looking and sounding, black mole is rich with coffee and chocolate aromas. This means the mole needs a meat that can stand up to it, like duck, version or kangaroo.
Wash this all down with classic Mexican drinks

Black mole with duck, caramelised figs and farro and pistachio pilaf.
A few years ago "fermented pineapple drink" would have sounded like an exotic or witchy elixir—these days, it's something many of us wouldn't bat an eyelid over drinking, and some of us would try making. If you're one of those keen to try making it, this refreshing tepache is a great place to start.

Mexican pineapple tepache. Source: Murdoch Books / Rob Palmer
Agua fresca translates to "fresh water", but may more accurately be translated as "fancy water"—particularly this one, which combines water with peaches, agave syrup, lime juice, mint and lots of ice.
Wrap up with something sweet

White peach and mint agua fresca. Source: Michelle Crawford
Bright paleta shops, in all their pastel-coloured decor, fruity popsicle-filled glory, can be found throughout Mexico. Paletas come in several different categories—fruit, cream, cream and fruit. This one is from the latter camp, and uses an age-old winner of a flavour combo.

Strawberries-and-cream icy poles (paletas de fresas y crema).
Horacha is a Mexican rice drink available from street vendors. Here, it's turned into an elegant panna cotta.

Mexican horchata, made with almond and rice milk panna cotta. Source: Benito Martin