If you plow through the materials for selling on Amazon, you'll probably feel quite overwhelmed. There is just so much info and seemingly endless requirements and fees.
I will be using amazon.com as the example since it is the biggest and most used of Amazon's marketplaces. However you should be aware that Amazon also operates in many other countries such as Canada (amazon.ca), the UK and other European countries, Japan, China, India, etc.
The main things you need to do are:
1. Get a bank account in a country so you can receive payouts from Amazon.
"To receive funds, you must provide a U.S. checking account or a bank account located in the U.K. or any country in the eurozone (Austria, Belgium, Cyprus, Estonia, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Malta, the Netherlands, Portugal, Slovakia, Slovenia, and Spain), Australia, New Zealand, India, Hong Kong or Canada" (From http://www.amazon.com/gp/help/customer/display.html/ref=hp_left_ac?ie=UTF8&nodeId=1161250).
If you don't have a bank account in any of these countries, then sign up with Payoneer to receive payments. This is what I'm using from Singapore. (Update, March 2016: Amazon can now payout directly into many more countries, however their currency conversion will cost you 4%-5%. It is much better to use WorldFirst and Payoneer to minimize foreign currency costs and maximize profits. I explain how to do that in this review: Getting Paid - Payoneer vs WorldFirst.
2. A US address for Amazon.com. This was a requirement when I registered an Amazon Seller Account in 2013, however it seems that this is no longer required if you sign up to sell by FBA since that means Amazon will take care of customer service and returns. If you need one, there are numerous mail forwarding services which provide a free US mailing address such as Viabox.
3. This is especially for non-US based sellers - sign up for a free account with My Inventory Team (MIT). MIT provides receiving, prep and forwarding of products for Amazon FBA. I currently send a couple of hundred items every week to MIT
Now comes the REAL work - sourcing. Sourcing is the key to a successful retail business on Amazon and involves lots of research. It would be way too much try to explain product research, Amazon category sales ranks, Amazon fee calculations, retail arbitrage, wholesale buying, private labeling, thrifting, shipping estimations, prep requirements, costs and processes, labeling, poly bagging, shrink wrapping, shipping domestically and internationally, customs, import regulations, inventory management and taxes here.
There's lots of free information all over the web, but if you don't want to spend the next 12 months reading theory and would rather get selling asap, I highly recommend the Proven Amazon Course (PAC). I bought it at the end of Oct 2013, sold my first 3 products in Nov. The materials (videos, eguides, free books) are all fantastic resources, but the greatest thing about PAC is the amazing community that helps each other in the Facebook group and forum.
Here's some proof that the Proven Amazon Course works! Below are my sales figures from Feb-Jul 2014. My goal is $20,000 in 30 Days Sales by end Dec 2014. The reason I post these figures is to encourage you that if this is possible for someone living on the other side of the world, who has never physically seen or touched 99% of the products I sell, you can do it too!
PS. You can also have a look at my PAC review.