Zoom blur is a funky technique where you zoom the lens while the shutter is open. This gives a funneling effect. You should choose a subject that is symmetrical or has a strong point that you want to zoom into. This will be the only clear part of the image. The surrounding area will blur down to the point.
Make sure you have a relatively uniform background with texture. You need to have something that will give the streak effect when you zoom.
I typically use a shutter speed around 1/15th of a second or slightly slower in shutter priority. Aperture doesn’t matter so much except to get a good exposure.
A tripod is very helpful as it allows you to keep a steady focus on the subject while you quickly zoom the lens, usually wide to telephoto.
Some of my students have come up with pretty cool effects!