I have a simple \"Hello Android\" application on my computer (Eclipse environment), and I have built an APK file. How do I transfer the APK file to my Android phone for test
If you have access to a Gmail account on the phone then an easy way (in terms of minimal set up effort) is to mail the .apk file to that Gmail account.
If you then access that account from the native Gmail app on the phone it recognises that the attachment is an app and offers an "Install" button.
As per other responses this approach also requires that you have selected USB debugging on the device.
Try this - it is remarkably easy ;-)