Panning is a technique that allows you to follow a subject (typically a car) moving in a straight line parallel to you. You need a shutter speed generally between 1/8 and 1/15 of a second. Focus on your subject, click and pan with the subject. It will take a lot of practice! Don't be discouraged, though hard to achieve, it is a fun technique!
Zooming is a technique similar to Panning but used with stationary objects. Keep your shutter speed around 1/8th to 1/15th of a second, focus on your subject and shoot on continuous while zooming in or out with your lens.
It creates an unusual but fun effect! If you are having trouble getting a slow enough shutter speed, make sure you are using a smaller aperture, your lowest ISO and if you still need to reduce it, toss on your polarizing filter!
If you are getting comfortable with your camera and are ready to try shooting in Manual mode, my best advise to you is to shoot in Manual mode! Just remember to pay close attention to your light meter and be aware of what it is telling you; are you over or underexposed? I like to give my students a short checklist to help them get started:
#1: White Balance- Where are you? Choose the most accurate preset or create a custom WB.
#2: ISO- How much light do you have? Noon in full sun, go low like 100, rainy evening or indoors try starting at 800.
#3: Aperture- Are you trying to blur out the background? Use a large aperture (small number). Need a lot of focus, use a small aperture (big number).
#4: Shutter Speed- Is it fast enough to stop the action of your subject? If your shutter speed dips to 1/30th or lower you should increase your ISO.
After these become second nature you can add on things like exposure compensation, changing focus modes, etc. And of course whenever necessary you can change your drive or white balance.
Another important thing to remember is that when shooting in Manual, you are not required to use Manual Focus; so many of my students have been under this assumption. Use Auto Focus when ever possible! I only switch to manual at times when shooting macro and my lens is having trouble finding my subject.