This is the basic instructions that I used last week to get HelloWorld on NodeJS on an Amazon Web Services' EC2 instance.
http://iconof.com/blog/how-to-install-setup-node-js-on-amazon-aws-ec2-complete-guide/#createAccountStill not 100% what the detail is about the payment, but I believe you get a free instance for a year. We shall see.
The main change from those instructions for me, was that I used ssh on linux to connect (none of that putty stuff) so I can't confirm whether any of that worked, I also had to set up a security group for my port (otherwise it blocks the port), it doesn't let you listen on < 8000 without admin access I believe.
So to get around all of this, I opened my helloworld listening port on 0.0.0.0 on port 8080 and this worked. (Be aware, that if you stop and start the instance again, it will give you a new address.)