Here is a guide to conquering the Aztecs which will give a general overview of how to maximise your success.
- Have their land discovered - your conquistador can travel through their territory unharassed, use that to uncover all the land you're about to own. It was changed in Version 1.3, you can no longer travel freely through their land. Try to uncover as much as you can and use conquistadors to explore after you declare a war.
- Have at least half decent reputation. Conquering pagan countries costs 5 infamy each, for three Aztec nations it will be 15 points in total, make sure it won't exceed your limit.
- Have the Deus Vult national idea - it allows you to attack the Aztecs without a stability hit, very handy, especially when you are colonizing heavily. So you should stop all your other research and invest all the money you can afford into getting level five government tech. You can also make up false claims on one of their provinces (the suggested one is Zacatecas, their CoT not to have your merchants hit after you conquer it).
- 12 to 16 units of cavalry in armies of 4k - you can do that with 8k if you're lucky and have good generals, don't hesitate to invest in at least one.
- Tolerance to Pagan set to max. You don't want them to revolt just after you annex them, do you?
- It helps to have at least one core province somewhere in the New World as you can train your troops there, without having to ship them from Europe. It is not required but makes things much easier. Even if you don't train your troops there, at least have a port somewhere near them to repair and station your fleet. Jamaica does well for that job. It's left uncolonized for many years too.
- If you create a claim in the capitals of the pagan countries you're going to conquer, you'll only obtain 2 infamy points for each country. Otherwise, the penalty is 5 infamy/country, which can be nasty if you're trade-focused.
- You must convert any CoT to your official religion as soon as possible in order to avoid the commercial penalty.
- Everything pagan you convert immediately after the conversion joins your state culture. Very handy if your nation isn't very numerous.
Land 2 your armies to the south of their Empire (Honduras) and have the third (and fourth if you're such a coward) army ready on ships next to the Yucatán peninsula to backstab them where they least expect.
There are 3 Central-American Indian factions allied to each other. Declare war on the Aztecs, they are usually allied with both other factions and also, if you proceed the way I propose, will be the last you annex.
It's important to check which nation took the leadership in the war against you. Annex it as the last one, as when you finish the war with the leader, the whole war ends.
Now you can attack. Ever heard of blitzkrieg? Do it. You don't need to siege as they don't have any forts built. Your cavalry beats their primitive infantry without a problem, so the battles aren't very challenging, especially with good commanders.
If there's too many natives in one stack and one of your armies fights with them for too long, drop everything you do with your other armies and send them to help the losing one. You can lose a province or two, but routing their biggest army is far more important than a province you can control again in a matter of seconds.
So you go and mark their land in stripes of your colour as quickly as possible. When first faction is all occupied, you annex them the same moment their last province falls and proceed to the second one. It's important not to hesitate here, their armies disappear immediately after annexation, so you have 10k of problems less.
When you annex the first faction and the second faction, go for the Aztecs, those who are the strongest and who have all the gold you came here for. They will have the biggest army and probably be the leader in the war. You don't have to get rid of their armies, simply rout them and chase them with one of your units, then just occupy the land with the rest and when it's all yours, annex immediately.
Congratulations, you're now the wealthiest nation in the world!