Good stuff above:
I am one who believes in the continental grip, good "quiet" ready position (racquet up, elbows forward of the body line, athletic stance with absolute neutral balance) and no fear (relaxed and smooth).
Continental because it eliminates need for grip changes. I know experts say grip changes can be made from fh to bh vollies. My question is why do something extra if its not necessary. Time is the biggest factor effecting how well a person volleys. Less is more. Plus in the continental one can "protect" to the bh side and almost all of the body and even to the hitting side of the body from the ground to the waist with a bh volley. Chest high and higher to the strong side necessitate a fh on reflex vollies.
Quiet ready position. Be ultra-ready but keep it simple and relaxed. Sometimes players, in an effort to be very ready and "on their toes" get very bouncy in the ready. When you bounce your eyes and vision bounces. You should "unwieght" as the opponent is about to make contact but don't bounce. If your vision is jarred you don't see the ball well. You can't hit what you can't see. Be relaxed at net but disciplined. Keep your racquet head up. Maintaining a 45 degree angle between the forearm and racquet shaft is a good reference point. Keep the elbows forward in the ready, in front of the body line. Not thinking about that can allow the elbows to slide back next to your sides or further back than that. Turn the shoulders with the elbows back and the racquet comes back with you and ends up next to or behind your body line instead of out in front. You end up taking the racquet back w/o taking the racquet back. Elbows forward promotes "out in front". Less movement. Less is more.
Even balance. Check your ready position when at the net. Many players while having a solid position to the naked eye are leaning, sometimes alot. Mostly the player will be leaning, almost falling forward. Be neutral. Truly be ready to move in ANY direction. Remember you volley mostly with your legs and feet. If you've already committed forward by leaning you really can only move straight forward w/o re-balancing and re-directing your transfer.
No fear. This goes hand in hand with a good ready position and being relaxed. Due to fear many players stand "taller" in the ready at the net. Its human instinct to protect the eyes and head. To be a good volleyer you must overcome this. With a continental grip and its upward angled wrist position at the net one's eyes should actually be closer to contact points on the volley than on groundies. Remain low, relaxed and close to the ball. Firstly you can always "save face" by a turn or bob of the head in an absolute emergency like a batter gets his head away from a bean ball in baseball. Secondly realize that no matter how hard a tennis ball is hit AT you, without a racquet in your hand, you should be able to catch it or at the very least get your palm(s) on it in the attempt to snare the ball. If you don't buy that, try it, you'll see for yourself. When you come to the realization that you can catch the ball with your bare hands at the net you'll understand that you can get your racquet on every ball hit at you. In fact another "hands and feet" drill is to practice "volleying" w/o a racquet. Have a partner feed balls from a hopper to you at the net. Work on catching the ball with the hitting hand. It teaches you that you must move your feet to every volley, volleying with the legs and feet and also the proper "quiet hands" technique which is the basis of volley technique. That's how active the feet should be and how quiet the hands should be when volleying. It's a good drill. Stay relaxed. Tension is a killer. A sure sign is when you begin to grip the racquet like a vise. Maintain your form and positions but don't muscle them. Tense and tight is SLOW. Relaxed and loose is FAST.
*Good players know they will get tagged from time to time. Like others have said accept it. It's only a tennis ball, no need to fear it. It's not a baseball. The only concern is against lesser players who blast without control or "headhunters" where a ball striking the eye is a greater threat but even then a turn or small movement of the head will save you from that threat.
As far as drills for reflex vollies the wall is good as BB told you. Another excellent drill is to place your hitting partner and yourself as close to the net as each of you can be. You can get it down to touching racquet tip to racquet tip across the net nearly to "shake hands" distance. Hit volley to volley. At those distances you can't hit hard. Its all about balance, reaction, balance and control. It forces you to return to a good ready position, maintain extremely quiet hands and to use your feet. No fear because the ball has to move relatively slow, but everything has to be quick, compact and balanced. It also forces you to focus on the opponent's contact to pick up direction a.s.a.p.. As you progress add more distance and pace, but add pace with your feet and legs moving into contact not by adding racquet motion. Think of catching the ball on the strings on all vollies. You can do the drill head on or x-court to bolster doubles technique. Another beauty of this drill is while you need a partner on the same page, it can be done anywhere, a backyard, outside the fence when waiting for a court to open up or in the basement or garage, you don't "need" a court to develop these skills.
With this drill you'll be speeding reaction times without sub-sonic boomers coming at you. Remember the proper balanced ready position, that less is more, relaxed is quick, catch the volley because you can "catch" almost any ball and vollies are hit with the feet and legs. Once you achieve the quiet, short and simple technique, reflex vollies won't seem nearly so daunting.
Good Luck.