Q:

What to look for in an overseas equity agreement

I am a US web designer currently negotiating a project with a Chilean company that would pay in equity.
I have never worked with anyone outside of the US, nor have I worked for equity, so my question is twofold:

What should I be looking for in an equity agreement?
Caveats on overseas agreements?

A:

Adventurer Beware!
Equity deals can be tricky things and I've never had great experiences with them but I have had two, and with those, I've learned a lot. 

The first thing you need to know (and you should - but you didn't put this in the question so...) is this an established, profitable business?
Often, equity deals going to non-investors are because the business is brand new (less than 2 years old) or is not (very) profitable. This can be a lot of risk you're taking on depending on how many hours you'll put into this gig a year. 
If the business can't show you that they're profitable and you're not emotionally invested with their service/product's success: don't take an equity deal...or at least not a straight equity deal. 
I tried, semi-successfully, to profit off of hourly & equity. Let's do some math. 
Say you charge, to make it simple, $10/hour. You'll put 10 hours a week for 52 weeks for a total of 520 hours a year, grossing you $5,200 annually. You negotiate to work at a discount as well as equity so that in the event the business is not (very) profitable it won't be a total loss to you. Let's say you give a 50% discount so you charge $5/hour. That's $2,600 annually and $2,600 you need to make in equity to break even. 
They offer you 10% equity. That means the business needs to profit $26,000 annually for you to make your $2,600. This is where data really helps. 
What did they make last year? What are this years realistic projections?
Did they net more than $26,000? Did they net a lot less?
This will help you get an estimate as to how much you're potentially going to make or lose initially. 
If the numbers don't add up and you're going to make less than your expected $5,200 a year - that's not always a bad thing. Businesses need time to grow. It's up to you to determine how much under your yearly estimate you're willing to go as well as how much potential you believe the business has for growth. 

Let's talk straight equity
They may not be too keen on a discounted hourly rate as well as equity or it may be more profitable for you to take a straight equity deal. 
As mentioned above

If the business can't show you that they're profitable and you're not emotionally invested with their service/product's success: don't take an equity deal

You need to be your own judge in this. They're many businesses no one thought would succeed and that were not profitable at one point, but are now some of the most successful businesses. If the business isn't profitable but you think they have something special going on then you may want to put in the blood, tears, and sweat for the long-term investment. 

What to look for in the deal
You decided to take the equity offer into consideration, good for you! How do you know it's the right one?
What type of equity are you getting?
This determines things like taxes and not all types of equity are equal. 
Look for red flags
If they don't explain exactly what holding equity in their business means for you, how they do it (each business does equity packages a little differently, and if they can't answer a question they need to be willing to research and follow-up. Equity isn't as simple as "Here's 10% of our quarterly profits". 
Can you afford to work for equity?
Maybe they offer you 50% hourly and x% equity. If that equity amounts to $0, are you financially stable enough to brush it off? Do you have more sources of income to make up for the loss?
I usher you to be careful and plan accordingly. Do as much research as you can and make sure you have a thorough discussion with the business. If this is a new business and the upper managements first business - chances are, they don't even know what fully goes into an equity deal. 

DISCLAIMER: 
I'm not expert in equity deals and I can't guarantee that any venture will be a success. I do have a limited amount of experience working for equity as well as a degree in business.

