Below are some links. The first is the Google Maps API documentation where explains how to perform the signature of Web Services. In it there are also examples in Python, C # and Java. The second is for a tutorial on YouTube where she teaches step by step using the signature. Remembering, as reports in the documentation, the signature serves for all services: Geocode, Directions, Elevation, Distance Matrix, etc.
Maps for Business: Generating Valid Signatures
To help validate that are generating the signatures correctly, you can use the following tool: https://m4b-url-signer.appspot.com/
Remember that to generate the signature is necessary the Client ID and the Crypto Key are in the welcome letter from Google.
URL to be signed:
Your private key: your-private-key
The limits of Web Services requests can be found in the following documentation: