Android: Download Eclipse (Windows, Linux or Mac) and the Android SDK (Windows, Linux or Mac) - no accounts or registration needed for either of these. In your phone menus enable development and connect via USB. In Eclipse make your hello world project, and hit Run or Debug. Enjoy.
Apple: You must buy a Mac. In the App Store (requires an account) or the developer site (requires an account and registration) download Xcode. Create your project. Connect the phone via USB. Right click to enable it for development and then do some song and dance with Apple to get permission to use "your" device for development. (I haven't yet worked out the exact dance required and how much it costs.)
I don't know what it looks like for WP7 but assume it is substantially similar to Apple.