I am not too familiar with the lightweight markup language used by github when updating README files.
Where are the resources which I can read up on how to write the appropriate markup syntax for my open source library's README/wiki files?
And is there a tool which I can "review my docs locally in my browser" before pushing the updated README to my github repository?
There are many Markdown dialects, the documentation for Github's can be found on the Github Flavored Markdown page.
nice tip from that page:
press M on any Github page with a Markdown editor to reveal the cheatsheet.
You can also use the Github Markdown Live Preview page to test your Markdown documents.
Update 2012-11-08: Efforts are underway to standardize the Markdown syntax. See The Future of Markdown - Jeff Atwood, Coding Horror and W3C Markdown Community Group.
Update 2014-09-09: CommonMark a markdown standard and spec has been released.