If you really want to learn to do this stuff yourself, I would suggest starting simple. Take a configuration management tool (I would suggest Ansible, which is a lot easier to use than Puppet of Chef) and an EC2 instance. Create, configure, terminate, rinse and repeat.
The simple fact that you can pretty much screw up everything you like, throw the whole system away and start again where you left off in a matter of minutes helps increase confidence and speed up learning, plus the configuration gives you a 100% accurate documentation of what you actually did.
But just like development, it's easy to get started but it takes years to master it.