We're not entirely sure of the time line here, but it looks like Google has now rolled out the SPDY HTTP replacement to its full bevy of Web services, including Gmail, Docs, and YouTube. If you're currently using Google's Chrome browser you're probably already using SPDY.
We originally reported on SPDY way back in November 2009, when Google introduced it as yet another experiment in making the Web faster, like Go, Native Client and speculative pre-connections. Over the last 18 months, though, SPDY support has found its way into the stable build of Chrome.
The best bit, though, is that SPDY is an open-source project. HTTP 1.1 is a lumbering beast that needs to be replaced before low-latency real-time computing really becomes a reality, and SPDY is one of the best options currently on the table. To be honest, we're not sure why SPDY hasn't received more coverage -- it's awesome in every way. At the moment, though, the only way to help speed up SPDY's proliferation, is with an experimental Apache mod.
As far as actually 'trying it out,' your best bet is downloading Chrome, hitting up some Google sites, and then checking chrome://net-internals to see your active SPDY sessions. SPDY is a transparent replacement for HTTP, though, and as such it's rather hard to see its effects. Google's sites definitely feel fast in Chrome, but there are more technologies than just SPDY at work.