I've been reading about lenses, studying optics applets, etc., but I'm still missing how to figure this out:

I have a regular, 35mm film camera with a normal, 50mm, lens.  What are my options for placing a lens element in front of the regular lens (away from the film plane), to achieve either a more telephoto (longer focal length) or a more wide angle (shorter focal length) image?  I just can't picture in my mind what the rays for such a setup would look like.

I'm aware that one can place magnifying adapters between the camera's lens and the camera body, but I want to work with a camera whose lens cannot be removed.

I have a few different camera lens assemblies for my 35mm camera I can experiment with.  I have experimented with various arrangements without achieving a useful effect.  There is probably a simple answer staring me in the face, but I'm having a problem conceptualizing it.

My ultimate goal is to experiment with a digital camera, placing some lens in front of the camera's lens.  I have a Canon PowerShot A580.  The lens is a 4x zoom, 5.8-23.2mm, 1:2.6-5.5

Why would I want to expand on the capabilities of my Canon point-and-shoot?  I need more control over image magnification, and I want to better understand the optics principles involved!

I mentioned the 35mm camera first, because I have more pieces to experiment with.

I have purchased an assortment of 38mm diameter lenses from Edmund's Scientific (double-concave F10, F15, F20; double-convex F5, F10, F15, F20, F30) and have a few other larger diameter lenses I've collected over the years.

What's the concept that I'm missing?  Thanks!