How to do strength training for martial arts is not a straightforward question. There are many different styles of martial arts, and each has their own characteristics.
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But once you know what aspect you want to improve in your art, it can certainly be done. It just takes some work.
Below you'll find some guidelines for what kind of training to do for grappling, kicking and punching arts, weapons systems, and internal arts.
Here are a few things to keep in mind as you read the information below…
Each style of martial arts engenders a particular body development style for its practitioners. For a really extreme example of this, compare Sumo wrestlers and old-school Tai Chi practitioners: radically different approaches to training, in both technique and conditioning exercises, that are designed to create 2 completely different body types.
When you're strength training for martial arts choose a method of conditioning that dovetails with your style. If you have any questions about this, ask your instructor for advice.
Many strength training exercises for martial arts closely replicate movements that you need for your art. When adding more weight and making your exercises harder, make sure you don't add so much that your technical skills get re-trained by your strength training movements.
For example, in Japanese swordsmanship there is a practice of using weighted wooden swords called Suburito to build strength and stamina. However, when training with these they fatigue you rapidly and the first thing to go when you're fatigued is technique - you begin cheating, using muscles you shouldn't, and the kinetic pattern of the sword swing gets distorted.
And if you do a lot of suburito practice mindlessly, you can distort your own good technique into bad technique. So, practice mindfully and don't practice to the point of crappy technique.
If you have any questions about how your strength training for martial arts might effect your technique or practice, ask your instructor. They should be able to give you advice in this area.
Grappling, whether it's BJJ, Greco-Roman wrestling, or Mongolian wrestling, depends on strength, grip, and an understanding of how to use the ground. Techniques of using the ground are mechanics of the art that you duty, but the full body strength and grip strength you need can be worked on.
Grip strength training is a must. There are so many actions that require grip strength, from applying chokes and holds, to effectively moving your opponent. If you what to become really good at any grappling style, you need to develop a strong grip.
Leg strength is necessary too, since you are constantly using you legs to move around, fend off, and even choke your opponent (or partner). I especially like the kettlebell swing, since its hip movement is so similar to the explosive hip escape movement in BJJ.
Basically, make sure you strengthen your hips and legs along with he rest of your body. The ability to generate unified full body strength and force can be done through Olympic style lifts, and will really help your game.
Explosive leg and arm movements are what you need to be working on here. Strong wrists as well, so that you don't hurt them when you're punching.
Doing clapping push-ups or fast punches with light weights to train speed are some good general exercises to try. They train the explosive chest movement of the punch.
Speed decreases a lot with fatigue. So you'll want to train speed for very short periods of time, with good, long rest intervals, to keep getting faster.
Add some endurance exercises as well - so that you can apply your speed well into any matches that you compete in. Speed and power are worthless if you're too tired to use them.
Also, focus your muscular training on where the power originates for your art. Boxing has a very chest centric method of generating power for its punches (though you do get a hip turn in there), but it has a very different origin of movement than, say, the punches embedded in the pre-arranged forms of Shotokan Karate - which have a very visible hip-centered origin.
Strengthen the muscles that are important for your art's movements.
There are tremendous differences in the strength and abilities needed in weapons systems, since there are tons of different weapons; Broadsword, foil, épée, and saber (and rapier) in fencing, the Japanese sword, archery, spearmanship, glaves, and esoteric weapons like the sickle and chain (kusarigama).
One aspect that I have seen overlooked during my training in Japanese arts is weak hips and legs. Since your weapons are held in your hands, doing arm strength exercises, suburito (heavy, wooden sword) training, and other upper body exercises gives you a more obvious benefit.
However, leg strength and speed are vitally important for closing quickly with your opponent and executing fast footwork. Don't overlook this.
If what you are doing has a more sporting component (ex: kendo, fencing, etc.), strength training for martial arts using lighter weights and training for speed will probably give you to most short term benefits. If you want to do strength training for martial arts for a long time, to get the most results, work on full body lifts, especially Olympic lifts, which build strength and power together.
If you are doing a classical weapons system focus on full body lifts from the get-go, since these styles tend to incorporate more full body movements. Also, the movements may be slower owning to historical aspects (simulating moving in armor, not wanting to fall down in said armor on a muddy battlefield, etc.).
Also, many systems with weapons have aspects of strength training for martial arts built into them. Using heavy swords, spears, or other weapons is the most common I've seen, but there are probably other aspects of strength training that you can magnify and train in order to get better results from whatever style you do.
One Note of Warning: Make sure you don't overdo your strength training for martial arts with weighted weapons too much at first. Aside from training bad technique, you can develop chronic overuse injuries such as tennis elbow that are difficult and frustrating to get rid of.
Internal strength is one of those esoteric skills that only a few styles strive to develop. Despite their overt differences, Tai Chi, Bagua, Xingyi, Aikido, and some classical styles of Japanese jujutsu (ex: Takamura ha Shindo Yoshin Ryu) strive to develop a certain set of body mechanics, specialized movement, and internal muscle coordination that I will cover with the broad term 'internal strength'.
Strength training for martial arts that are 'internal' arts is highly style-specific and does not fall within the realm of western strength training.
My advice for training this kind of strength is to ask your instructor what to do to cultivate it, and then practice like a demon. This stuff is not easy to develop.
For example, Tai Chi forms are not a semi-arbitrary chain of linked punches, blocks, parries, and kicks. Those overt movements exist, but the overall style of the Tai Chi form is meant to retrain your body to move and react differently to forces, as tested in that sparring (called 'pushing hands') done in Tai Chi. This is the internal strength training for martial arts done in Tai Chi.
Of course, this applies only to 'martial' Tai Chi and not to the watered down version many people are aware of as practiced by the elderly to develop flexibility and concentration.
If you really want internal strength, (1) find an instructor that has it (i.e. find an instructor with abilities that you want to possess) and (2) find out if his senior students have similar abilities (i.e. Is the instructor actually teaching what s/he knows?). Then (3) practice hard. Damn hard.
While commonly described using archaic eastern terminology, internal strength is real and can be explained quite concretely by an instructor that knows it. Find somebody real, and work hard.
Oh, and be sure to sign up for the e-zine Starting Strong to get monthly strength training, exercise, and diet tips e-mailed to you - and access to the free e-book Train Smart, Eat Smart: Exercise Nutrition Hacks!
Strength Training For Martial Arts: Do It Right
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