From that page, select the region that you would like to access a server in and press the big Continue button
You'll need to do a little set-up on this next page, specifically setting up a Key Pair so that your instance is secure.
Once that's done, you should be able to launch your instance with the 1 click button
(yes, it has been more than 1 click and you still have a couple more but the sentiment is nice)
It should take 2-3 minutes to get your instance rolling so just be patient - if you've just setup your AWS account, it can take a couple of hours to get that verified (that wait was agonizing for me)
When that is set, you can download the remote desktop launcher from AWS, point to your key pair file and decrypt the password to login to your instance
You'll see a desktop something like this (I've actually shrunk mine down so it's easier to do a screen cap). From here, launch the software as you like.
Here's a short video clip of Maya running.
You have storage with the AWS account and instance so you can save your data between sessions. Here you can see a small MEL script I wrote. For the little demo movie, I made the character with Project Pinocchio and downloaded the file from my Autodesk 360 storage.
When you are done, make sure to stop or terminate your instance so that you're not being charged for further computer time. If you stop it, your data will be there for future sessions. If you terminate, you're wiping everything.
This is pretty cool to try out and does open some possibilities for how things may work in the future!
Should you want to know more, here are some additional resources: