Setting up an AWS account is about as easy as setting up an Amazon account to buy books, In fact, if you have an Amazon account, you're already half way to getting an AWS account. Once you have an AWS account you have to sign up for EC2 itself.
You will be asked to provide a payment method for Amazon EC2 services. These are charged on an hourly basis (e.g., 9 cents per hour for a small cloud server).
Once that's done you'll need to get your AWS access credentials.
Once you have both your Access Key ID and your Secret Access Key, you're ready to move on to setting up your server on EC2. You simply cut and paste these alphanumeric keys into the field and then...
You pick out which level of service you want. Let's say you're just exploring. In that case you'll want either the Hobby option or try out micro servers. TurnKey Linux won't charge you a thing for its hobby option, but Amazon will if you don't use a micro-instance. If you want to pay the absolute minimum, go for the micro-server option. With it, Amazon won't charge you for your first year of use of micro-servers.
Next, you can either enable backup storage on Amazon's Simple Storage Service S3 cloud or start setting up your first server. TurnKey and Amazon gives you 10GBs of free S3 storage for starters so you can skip setting up an S3 backup until you know that you've got a server you really want to work with.