A simple sandboxed approach to trying out Razor is using the pe-razor-vagrant-stack. This uses several VMs in an environment where you can try out different commands and provision nodes.
The PE Razor documentation's command reference in addition to the built-in help on razor-client should help you get started. Once the node's facts have been submitted, you can write tags to match against and classify the node, create a repo for freely available OS's like Ubuntu Trusty and/or CentOS 7 (reference the respective included task for these), create a broker for what the node should do after provisioning (the No-Op broker, which is included, will do; just run
razor create-broker --name noop --broker-type noop), then finally create a policy to trigger the actual provisioning. More detail is available here.
Once you're ready to use Razor beyond this virtual environment, I'd start at the PE Razor documentation for installation.
If you hit any questions along the way, feel free to message here, the #puppet-razor mailing list, or on the #puppet-razor IRC channel on Freenode.