Jiu Jitsu is a grappling type of martial art. Therefore, the best exercises are going to be those that improve the person's ability to fight in this style. In addition to the need for muscular and cardiovascular endurance, necessary in any martial art, one also needs to work on improving grip strength.
Cardiovascular Endurance Exercises
Marcus Soares is a seventh degree Black Belt who studied under Carlson Gracie, legendary in jiu jitsu for his development of the Brazilian style of the art. According to Soares, no matter how good a person's technique is, he or she must have the endurance to keep fighting. Soares notes that cardiovascular workouts can help with this, and in particular running up hills. The key is to keep going and push yourself even when you're tired, as this is exactly what is required when fighting. Doing this helps to build endurance, toughen yourself mentally and teaches you how to deal with pain.
Muscular Endurance Exercises
Weight lifting helps to build muscular endurance and circuit training in particular is advised by Soares. In this type of weight lifting, you perform a series of exercises one after the other for different body parts before taking a break. An alternative to working out with barbells, dumbbells or machines is to use a kettlebell.
Joey Alvarado, a former mixed martial fighter and creator of Kettle-Jitsu, has developed special set of kettlebell exercises specifically for jiu jitsu practitioners. An advantage to this is that you can do a lot with just a single kettlebell in limited space at home. Care should be taken with swinging these as doing so improperly, especially if you are not ready for the weight, can cause injury.
Muscle Strength Exercises
These types of exercise focus on building strength as opposed to endurance. It is especially important to work on building leg strength as the legs play a pivotal role in jiu jitsu. Soares advises that squats are ideal for this as they not only build up leg strength but also increase your heart rate as you're working out. These can be done with a partner so that the person doing the squats drapes the other over his or her shoulders for weight. Military presses to work the shoulders, curls to work the biceps and pullups to work the back are also recommended.
For grip strengthening, Soares recommends the pullup. Most gyms have pullup bars and it's also easy to put one up at home. Alternatively, if you have a partner to work with, you can do row exercises in which one person lays down flat on his or her back and the other stands, straddling that person around the waist. The person standing can pull the other up by his or her gi. It is important that the person on the ground maintain a straight back. Other exercises can be incorporated as well to work on wrist and thumb strength.