Just 15 years ago Mexico won the war for independence against Spain. Fresh from that victory, in 1836 your game starts with a war against Texas. For all who remember the Battle of the Alamo, it should come as no surprise that Mexico can easily dispatch Texas. The problem comes when the gringos up North decide that Texas is their land!
Your general strategy can follow three routes: outright capitulation to the US with engagements in Central and South America, a middle strategy, or outright war with the US.
Industrially, the outlook is pretty grim: you have a very dispersed population. Your only population center is Estado de Mejico, with just 1.5 million people, many of who are priests or aristocrats. You have 3 small POPs as clerks, ostensibly waiting to be converted into Capitalists, but you are much better off creating a 50,000 POP capitalist to build your railroads. On the plus side, you should be raking in alot of money very early on due to basic commodity production and gold discoveries.
The Mexican-American War
In this strategy, you've either annexed Texas or made it a Sattelite (the better choice). The war will start with a US DOW sometime around the summer of 1843. Your basic objective is to take every US colony, and while the war is being waged, take the colonies the US trades with England. This will allow you to claim the Western US (Washington, Oregon, Colorado, Oklahoma). After you have all the colonies, you need to win the peace, and this means extracting a heavy toll on the US. It isn't easy. You will need a big pool of soldiers to be able to sustain yourself in this war long enough to convince the Yankees to give up the fight. The US AI has a very particular style, and if you study it you can be sucessful. By playing smart, it is within reach for you to win the peace within 4 years, be a world leader in prestige, and don the mantle of a "Great Power". While war will become a fact of life with the tenacious Americans, the rockies provide excellent defensive bases, and the key is to hold out until the US Civil War.
In 1859-1860, the US Civil War will occur, along with the forgiveness of any national debt you may have (if you let relations with Europe drop too far, they will DOW). So long as you are poised for the outset of the war, allying with the CSA is an important opportunity for limiting US expansion. Unfortunately, however, as a result of the wars you've been fighting with the North, the US has built up a large army. Thus, when the CSA appears, it will be incredibly weak by contrast. A European Ally such as France will be a great help during the Civil War, and with a great deal of skill and luck you have a chance of winning.
The Sleeping Fox
An alternative, relatively easy strategy, is to start by humilating Texas only, and taking a friendly approach with the US. The Texas humilation will catapult your prestige, which you can maintain with cultural research. You'll need your Great Power status to go on a diplomatic blitskrieg with France, England, and Spain. You can quietly and easily grab Central America, create a capitalist to start churning factories, and build up a massive pool of manpower.
In 1861, the CSA will appear, and the US won't be prepared to fight a two front war: with their new enemies from Mexico. Allying with the CSA in this strategy, you can smash the US fairly readily. Waging the war long enough and you should have no problem making the US a sattelite, or whatever other spoils of war you choose. The only downside to this strategy is that it is pretty easy, and therefore, a bit gamey.
The Peaceful Strategy
A third strategy for Mexico is to maintain excellent relations with the USA. Perhaps going so far as to trade land for money and technology whilst expanding to the South at the expense of it's weaker neighbours, perhaps snatching Spain's remaining American outposts along the way.
A Great Power finish should be the objective here, Superpower status will be almost impossible to achieve. At the end of the game, it is possible for Mexico to be one of the most educated countries in the world, and in the top four in both reputation and industry.