I've been very focused lately on endurance training (especially power-endurance and speed-endurance) for several reasons.
First, I've been extra focused on losing bodyfat, and the greater your endurance the greater a workload you can handle, and the greater workload you can handle the more calories you can burn.
Second, I find that, at least for me, one of the biggest impediments to sparring has been my fitness. When I'm tired, I get slow, and when I'm slow I'm not very good at fighting.
Third, I've been extra focused on my karate practice, and improving skills takes lots of repetitions done while fresh (practicing karate while fatigued is somewhere between less productive and outright counterproductive). If you want to get better at a movement, you have to practice it while fresh, and the better your endurance the more fresh repetitions you can get, and the better you'll be.
Anyway, just like strength training, endurance training is complicated and very individual. If you can afford to hire a really good conditioning coach, that would be better and more efficient than what you can implement yourself. However, even if you can't get expert help, there might be room to improve your system. A lot of training programs are less effective than they could be. People often think that any hard workout that causes suffering will improve endurance. I'm not going to pretend that you can get fit with NO suffering, but results aren't simply proportional to how hard you work.
I plan to write more in depth about energy systems and the best general kind of plans for gaining karate in ways that correlate to traditional martial arts practice, but there is a simplistic overview that I think will be helpful for most people: High/Low.
Let me explain.
Suppose you can do a certain activity for 30 minutes - sparring, kata practice, whatever. After 30 minutes, more or less, you get noticeably fatigued and can't perform well (or maybe you just collapse). And suppose that you'd like to be able to go for longer, or at least last longer while feeling fresh and energetic.
One way people will try to improve endurance for this activity is to just do more of it. So, if you can do 30 minutes of sparring, force yourself to go for 35 minutes, or do it several times a week, and hope to get better at it. Or, similarly, they will engage in a different activity that is just about as difficult (say, jogging at a pace that they can keep up for 30 minutes), and push that as hard as they can. And, often,
Now, don't get me wrong, this approach will work. It just won't work very well.
Why not? Well, a few reasons. Primarily, if you're already doing 30 minute sparring sessions, then adding another similar intensity workout to your week isn't really giving your body a new stimulus. And just extending the workout by 5 more minutes is all too likely to just get your body used to adding sloppy minutes to the end of your workout.
Instead, it's more efficient to force an adaption by adding two kinds of workouts:
1. Do workouts that are harder and shorter (greater intensity, less duration) than the work you are training for. For example, add some High Intensity Interval Training (quick example: do 3 burpees every 30 seconds for 20 minutes). Make sure the work periods are much, much harder (more intense) than the activity you're training for, but much shorter.
2. Do workouts that are easier and longer (lower intensity, greater duration) than the work you are training for. For example, do 60 minutes of continuous aerobic exercise that keeps your heartrate under 140 beats per minute.
In my experience, you should do each of these workouts at least once a week, and maybe do your target activity once a week (more is ok; much less is probably not ok).
By presenting your body with different stresses (harder, longer) than what your'e already doing, you'll force new adaptations from your system. And those adaptations will help you with your target activity - there is no such thing as mitochondria that only work at specific intensities, you either have more or you don't. So those adaptations will carry over to your target activity.
Give it a try for 3-4 weeks and see how much it helps!