Is there an easy method to send the app to my phone or do I have to do it using debugging from the development computer while being connected to the phone?
Also, do I really have to sign, version, prepare and publish the application before I can actually use it on the phone? Or, can I use it on just my phone without publishing it to the world?
Click the Run toolbar button, or choose Project|Run from the main menu, IIRC.
“using debugging from the development computer while being connected to the phone” is “an easy method to send the app to my phone”.
All the necessary steps are handled for you by clicking Run.
Whether you use Eclipse or command-line tools, you can push your APK into your phone without publishing it to the Android Market.