What he said
Actually there is one other requirement depending on how Android is set up on the phone. It needs to allow non-market apps to be installed. On my phone this is under "Settings > Security > Unknown Sources" If I don't check this it won't allow me to install the program after I download and click on the .apk file.
Warren good suggestion, I'll see if that is somehow possible in the App Inventor IDE. It really is very basic in its capabilities but it may be possible.