The CycleStreets Android App is available through the Android Market. Like other apps, if you install from the Market, you will be informed of new updates as they are released. Unlike most other apps, the CycleStreets app is free software - the code is available for anyone to poke around with, build on, add to, and so on.
The code is more or less constantly evolving, so there are often new features or bug fixes in the code some time before a release to the Android Market. Features or bug fixes you might like to have. Of course, not everyone has the time or skills to build the code themselves. Fortunately, we have software to that for us.
Each time I make a change to my copy of the app's code, a new build of the app will appear here. Whatever I'm working on might not be entirely complete, but it'll be the very latest code there is.
Once I have finished a feature, I push the code into the main branch. Those builds will appear here, in the master directory. Builds of this branch will happen less often, but new features should be complete.
To install any of these builds, you will first need to uninstall any existing version of the CycleStreets app you might have on your phone, and then turn on the "Unknown sources" setting. With that done, download the build and, once the download completes, select it. Your phone should offer to install it.
Unfortunately, there's no way to automatically update an application you've downloaded like this. The best I can offer is an RSS feed of builds.