AppEngine
The site is implemented using Google AppEngine - see appengine.google.com for details.
Getting Started running schema.org locally
The Schema.org site is implemented as a small Python application for Google AppEngine. You can use it to test ideas for changes to the site (usually schemas, examples and other documentation; occasionally site functionality).
To make test versions of the site (on your own machine or for publication on appspot.com) you'll need to install a version of the AppEngine SDK. Windows, Linux and OSX versions are available. Make sure to choose the Python (2.7) version.
AppEngine is documented at https://cloud.google.com/appengine/docs but here are a few points that may help.
Environment
The local development version requires a Linux-like environment (includes OSX).
Get a copy of schema.org filetree from Github
Once you have AppEngine and Python working, grab a copy of the schema.org repo via Git - This is documented in the following file on Github: https://github.com/schemaorg/schemaorg/blob/master/SOFTWARE_README.md
Then you should be able to run it on localhost fairly easily. One possible gotcha there is anti-virus / security settings which might prevent you running a local server.
The usual way to do this is by running "git clone --recurse-submodules https://github.com/schemaorg/schemaorg.git". If you do not have git on your system there is also a zip download: https://github.com/schemaorg/schemaorg/archive/master.zip
Once installed, a local version can be started by running the ./runpythonapp.sh script in the created schemaorg directory.
For more details see https://github.com/schemaorg/schemaorg/blob/master/SOFTWARE_README.md