AWS has 100's/1000's of options. AWS is their umbrella name but each service has it's own pricing. Check out »
aws.amazon.com/pricing/ and you'll see all the services. As an example, EC2 is their cloud based server offering (pricing at »
aws.amazon.com/pricing/ec2/ ) and S3 is their cloud based storage offering (pricing at »
aws.amazon.com/pricing/s3/ ).
You pay by usage. Storage usage is measured in GB. Server usage is measured in hours you have a particular server instance active.
On the server side you have an "on demand" instance or a "reserved" instance. A reserved instance is useful if you will have something running full time over the course of a month/year. You pay less for a reserved instance. On Demand instances are good if you need to spin up a temp server for testing or when load demands additional capacity for a somewhat limited time.
Start with »
aws.amazon.com/free/ to check things out paying attention to the limits for each of the services included in the free tier.