What is the best overall way and types of exercises that can help? For exercises, how long and frequent? My body build is that of a female East Asian, and it is rather difficult for me to gain muscle, especially in the arms (think of the goal as strong punching and kicking strength).
Generally, training for muscle mass involves relatively high repetitions per set and high volume (total work), while training specifically for strength involves heavier weight and fewer repetitions per set. There's a lot of overlap, though, even in the extremes of the fitness world: In theory, bodybuilders, for instance, don't care about strength, but increasing weight lifted is an invaluable way to 'challenge' a muscle to grow as it gets stronger.
Keep in mind that muscle size isn't directly related to strength. A person with skinny arms might be able to press much more than a person with developed arms...or think about it this way: A bodybuilder might spend 3 years to gain an inch of muscle on his arms and 50 pounds of pressing strength, but a person training for strength as well might spend 1 year to gain the same 50 pounds but only a fraction of the muscle.
In your case, training for both mass and strength/power would be best achieved through relatively heavy compound (multi-joint/multi-direction) movements performed frequently, maybe 2 or 3x/week per movement. Your goals are typical, and the movements and workout scheme I'm prescribing are pretty universal because they're so effective.
- Squats, deadlifts, push presses/push jerks, dumbbell presses, dips, pull-ups, etc. would be some of the most valuable movements to learn
- Generally avoid 'filler' movements like dumbbell triceps extensions or chest flyes; will lead to more soreness (slower recovery time) and these are poor strength builders
A good workout might last 45 mins to 1 hour and consist of:
- A full-body warm-up
- Barbell push press, 4 sets: 8, 3, 2, 2 reps
- Push-ups, 3 sets to failure
- Barbell back squat, 4 sets: 10, 10, 3, 3 reps
- Rear-foot elevated squat/split squat, 2 sets per leg: 12, 5 reps
Here there are challenging barbell movements (push press/back squat) followed by movements that target individual muscles more directly for added hypertrophy. And as the number of repetitions decreases, weight lifted should increase. A set of 2 reps should be difficult.
If you want to punch or kick harder, use a punching bag in addition to weight training.
Eat plenty of carbs, salt, protein, and fat to gain weight. I don't have much experience in the nutrition department, but weight gain is as simple as calories in/calories out. Get plenty of sleep, aim for ~1 gallon of water per day.
Keep workouts simple, frequent (5 to 7 days/week; perform given movements 2 to 3x/week as I said earlier), free of fluff, focused on wholesome, compound movements that keep the core strong. If you're lucky enough to have tires to flip or ropes to climb, include some of that. And I could write a few paragraphs on this, but avoid selectorized machines, as they often force the user to move in unnatural ways and don't allow muscle groups to work together properly.
Use good technique, heavy weight, and tear it up.