I describe how to do this, according to the way that WRI provides, in an essay at my web site. You need only the first part of the essay.
Essentially, create an application in your $UserBaseDirectory/Applications
directory and put your package there. If you have any other resources such as a palette your can also place it in your application. You can place everything there and Mathematica will automatically know how to find it. You don't have to use any Mathematica Install Palette operations. You can also have more than one package file there if you wish. It's all very simple and standard and yet users seem to get drawn away from it for no good reason at all.
You can also easily send the entire application to any other Mathematica user and they can install it simply by unzipping into their Applications folder.