Stable version is recommended for most of the users. There is a good chance that your Linux distribution includes Tomboy. Refer to your distribution's software installation instructions.
You can also install Tomboy from source code. Note that you then need several development packages.
Development version is meant for developers and for those who want to try out the latest features and improve Tomboy. This version is likely to have bugs. Please help us to track'em down. Visit the Get involved page.