Our Getting Started guide gets you up, running and debugging a "Hello world" Service Worker in Chrome. If you are stuck the FAQ may have the answer you need.
Blink's Service Worker V1 - scope and status describes the initial scope of features we are targeting, tracks the implementation status in Blink and provides a high level overview of changes.
Is Service Worker Ready? tracks the implementation status of Service Worker at a fine-grained, feature-by-feature level in many popular browsers.
Go to http://crbug.com/new and include "Service Worker" in the summary. You should get a response from an engineer in about one week.
If the browser crashed while you were doing Service Worker development, go to chrome://crashes and cut and paste the Crash ID into the bug report. This kind of bug report is very valuable to us. (If you do not see crashes in chrome://crashes it may be because you chose not to send usage statistics and crash reports to Google. You can change this option in chrome://settings .)
...interested web developers are welcome to poke around too!