The Polymer Project offers a range of tools for developing, building, and optimizing Polymer elements and apps.
You can use Polymer CLI for the vast majority of your Polymer development tasks. Read Polymer CLI to get started.
For use cases Polymer CLI doesn't handle, you can customize your toolchain. Check out Advanced tools for a description of the underlying tools that Polymer CLI is composed of, and then use a build tool like Grunt or Gulp to automate your workflow.
In addition, the Services doc lists some web services that you may find useful when developing with Polymer (such as the Polygit development CDN for rapidly prototyping elements).