I am by no means the senior most martial arts instructor in the US; geez, I'm not the most senior in my school, but having taught for over ten years, I have observed some keys that separate the successful from the struggling martial artist.
Show up - There are two parts to this. First, far too many students try to build their martial arts skills one night a week, or by attending three classes right in a row when they know a test is coming. I realize that busy work and school schedules often prohibit attending four or five times a week, but one class per week is probably not going to cut it unless you are doing some serious self study at home. Try to attend at least three times a week, even if some weeks you can't keep that schedule - set that as your goal. Secondly, when you show up, be there. Don't bring your school work, or business problems with you, concentrate on the martial arts class. In other words, when you show up, show up.
Relax - Sure, martial arts is about using your body to produce or control power in ways you wouldn't image, but that doesn't mean tightening all your muscles. In fact, relaxing your muscles until the exact right moment not only enhances your power but also improves endurance and stamina. Simple exercises can help such as making a tight fist while keeping the bicep (upper-arm) relaxed. Practice all of the stances your instructor teaches you in a very relaxed manner, learn to be loose.
Compete - Some practitioners love tournaments, other tolerate them, and the remainder despise them. The key to tournaments is not to expect too much from any one; rather, participate in many of them. It really doesn't matter if you win or lose, it's all about the preparation. The more you go, the more you'll have to prepare, and it's in the preparing that you get really good.
Breathe - Inhale as you begin each technique and exhale (usually very quickly) as you execute. Learn to breathe deeply, slowly, and with control. Having difficulty with a new technique? Slow down and breathe. Can't break that board? Review your breathing from preparation through and including the Kiyup (Spirited yell) as you strike the board. Oxygen fuels the lungs, the lungs fuel the brain, and the brain controls the body. Breathe.
Stay - Obvious alert! If you quit your martial arts training you'll never progress. To be sure your improvement as a practitioner will decrease as you progress through your training. The delta you experienced as a novice white belt will seem huge compared to your improvement as a red belt - this just makes sense, right? You will get discouraged as you plateau from time to time. Stay. Continue to train, and you will get better, and while you might not feel improvement, rest assured that is is impossible to train hard and not improve.
Teach - Want to get really good? Teach. As a teacher you necessarily need to focus on minute details as you explain positioning, balance, waist twist, extension, and techniques. This will in turn become more ingrained in your execution. Teach, and you will become a better student.
Understand - So you've just learned your new form/pattern/hyung/kata. What is that crazy move where you seem to grab, twist, and jump (I made that up)? If you cannot figure out the meaning or significance of a series of techniques, ask. First, try to figure it out. Imagine how a block, attack, feign, or move might be used. Some techniques have no practical application but are useful training aids to build balance, strength, power, or flexibility. Others have very practical application. Try to understand why, when, and how.
Emote - Once you have learned how to strike or block, and you've begun to grasp the value of proper breathing techniques, the next level of execution will come from controlling your emotions. Like an actor who has to move from scene to scene in a play and exhibit various feelings, so too does a martial artist need to control and demonstrate emotions. There is no way to properly execute a spear hand attack (thrusting attack with straight fingers stabbing like a knife) without a corresponding mental state that resembles absolute conviction to success. Whether you call it anger, terror, or gritty determination - you have to place your mind in a state that says, "I am going to penetrate this obstacle (board, stomach, door, etc...) even if it costs me the use of my hand for the rest of my life - I AM going through." You need to be able to call up that level of conviction, and then let it go the second after execution and return to a state of calm. Learn to control, not be controlled by, your emotions.
Tight Fist - This sounds so simple; just make a tight fist. Now, don't let it go for the next hour. Relax your shoulders, and your arms, and your knees, and... but keep your fist tight. Make it really tight. The tighter your fist the more dense your strike. Do not open and close your fist and you move from technique to technique. Do not ever fight/spar with a loose fist. My favorite lesson for newbies is to palm-strike their loose fists (not too hard - I'm not trying to hurt anyone) and watch as they say immediately stop sparring. "Wow" they always say, "that stings." Yep. Keep your fists tight.
Low Stance - Different martial arts may have different perspectives on this one, but in Tang Soo Do a low stance is used to improve balance, power, and (believe it or not) height (for kicking and jumping). Low stances are also harder to maintain than high stances, so therefore, they tend to provide a better workout.
Concentration - This is a catch-22 of sorts as martial arts are supposed to improve concentration, so telling you to concentrate is like saying, "save money and you'll save money." We tend to get better at anything we practice with effort. The more you practice concentration, the better you'll get at it. In the context of karate, concentration usually includes making sure you're looking where you're supposed to be looking (very important in forms/kata/hyung/patters) and that you don't lose focus to distractions.
Well, there you have it, my top ten keys to successful martial arts training. I hope these tips serve you well, and I'm always interested in your feedback.