ChromeDriver is a Chromium project and the code lives in the Chromium repo. Chromium is the open source project which Google Chrome is based on. Follow the instructions for checking out the entire chromium source tree.
After you have your source checkout, make sure you have completed all the build prerequisites for your platform. Note, you do not need to actually build Chrome (which can take hours); you just need to get your machine setup properly. See the per-platform instructions:
In your source checkout, see src/chrome/test/chromedriver/README.md (latest readme)
Read about how you can file bugs at our issue tracker and read the mailing list.
See http://www.chromium.org/developers/contributing-code. Basically, use 'git cl upload' to upload your patch (which should be in its own branch) for review. Then go to the web interface and publish it to an appropriate reviewer. Take a look at the history of the file (and any OWNERS file) in determining an appropriate reviewer. The reviewer will guide you from there in making changes, using the try server, and committing the code.