Do I need to know how to swim?
Short answer = no. Long answer = you do not need to be a swimmer to dive. You should feel comfortable being in water. You will have the equivalent of a life jacket (called a BCD in dive speak) and a lifeguard (called an instructor in dive speak) so if you just want to try and see what all the hype is about you will have nothing to worry about!
Do I need to wear a helmet?
The helmet you are referring to is the type seen in old school movies and used for deep, technical diving. Recreational divers use a simple mask that covers the eyes and nose. The same as you would snorkeling.
Will I get water in my mouth?
No. The regulator, that thing that goes in the mouth, is full of air from the tank. When you breathe, it will be air from the tank. If you choose to take the entire course, you will learn to take the regulator out of your mouth for photos and learn how to get the water out (hint:same as snorkel).
Will I get water in my mask?
Possibly. The mask should fit snugly against your face. Your instructor will teach you how to test it by holding it to your face without the strap on and breathing in through your nose to see if a suction is created. Your strap will then be placed on your head.
The main mistake by novice divers/snorkelers is making the strap too tight. This allows water to seep in through the tiniest wrinkles created by smiling, laughing, any facial expression. If you do laugh underwater and get a small amount of water in your mask it is no big deal and the instructor will teach you how to get it out, or simply surface to empty it and descend again. If you take the class you will be required to learn how to empty your mask while underwater.
Why do I need weight?
Most people are positively buoyant (float). In addition, your equipment is usually buoyant. You will need some weight to counteract this to actually allow you to sink a bit to get under the surface of the water.
I think I am claustrophobic — can I still dive?
You should try. Once you are familiarized with the equipment and realize you will always have air, are able to surface, and start looking at some really cool things, you may find your nervousness disappearing and your enjoyment of the amazing surroundings taking over!
What about my ears? They hurt when I go underwater.
You will learn something new. It is a simple concept but never explained to people until they learn to dive. It is called equalization. These techniques will help you on a plane as well.
In short, as you descend (whether on a plane or underwater), the pressure of the water is pushing against your rounded ear drum. It is making it flat. This is what causes the pain. You simply need to add some air to the other side (inside) of the drum to keep it rounded. This can be done usually by pinching your nose and blowing gently as if you were blowing your nose. Others wiggle their jaw or swallow. All accomplish the same thing. A rounded, pain-free ear drum. Repeating this every meter/few feet will prevent any pain from occurring.