First things first, there's nothing called a docker instance. You have a docker container and that can be deployed on ec-2 (and other) instances.
There are two things you can do if you have your mind set on using AWS.
Use AWS's EC2 Container Service (ECS). They have a brilliant wizard setup to create a cluster and you pretty much just have to fill in the container configs (image name, ports to expose, environment variables etc) to have your container deployed. Also, the wizard ensures that the machines that get booted come with the necessary packages installed (docker for instance). Security groups, load balancing etc can be manged from the EC2 console. ECS is available in a decent amount of regions across the world, use the use that's closest to your customers. With ECS, you can see your container live in a few seconds.
The second way is to boot your own instance and install docker (And other dependencies). Manually set inbound and outbound traffic rules, pull your image and start your container. If I were you, I'll definitely go the ECS route mentioned in step 1.
Also, have you checked out Google Container Engine?