How to zoom using a Nikon D3200 camera?

The question is actually on zoom and focus

My brother said that I don't have to focus and just set the two switches on the lens to auto and for zoom i just let it zoom automatically

I think he's wrong about the zoom-i have to turn the lens right?

also, what mode is best for still photos of people in general? The costco guy said to use aperture

Yes, your brother is wrong

You are in charge of physically zooming the lens to the focal length you need to compose the shots.

Yes, any Nikkor AF-S lens attached to your camera will automatically focus for your shots.

Using aperture priority, you can define the depth of field when you take your shot.

Yes, you have to turn the zoom ring on the lens to zoom, the camera can't do this automatically.

The guy at costco was about right - aperture priority is a popular mode even among experienced photographers. You maintain the full control over the aperture, which is an important tool to affect the depth of field of the resulting photo. The camera automatically takes care of the shutter speed then and possibly also ISO if ISO auto is activated. That' often ok, as the shutter speed is uncritical in many situations unless camera shake blur or subject motion blur are an issue. Myself, i use a lot of aperture priority too, mostly in daylight situations. I use full manual mode, taking control of the shutter speed myself, in low light situations (where camera shake becomes a problem that needs to be compensated with certain minimum shutter speeds) and when i want to play with subject motion blur.

You have to turn the zoom ring to zoom. Your brother is wrong.