Running in a browser
For best results use a WebKit based browser (Safari or Google Chrome are recommended). Note: if you use Google Chrome you will need to launch Chrome with --allow-file-access-from-files --disable-web-security flags.
Next, checkout the source code and open the main index.html file in your browser.
svn co https://webos.svn.wordpress.org/trunk webos-wordpress cd webos-wordpress open webos-wordpress/wordpress.application/index.html
Simply edit a source file and refresh to see your changes.
Running on the Emulator
First you will need to download and install Palm's webOS SDK.
Once installed launch the emulator in 1024x768 mode (the resolution of the TouchPad). After the emulator is finished launching you can checkout the repo and install the app onto the emulator. Pull up your command line and enter:
svn co https://webos.svn.wordpress.org/trunk webos-wordpress cd webos-wordpress ./install
WordPress for webOS should now be running in your emulator window.