well, there are a few simple things you can do, such as a reasonable but consistent number of pushups and situps/crunches every day. I personally get bored with a full weight lifting routine, so I just stick to something small that I know I can do quickly and easily. These exercises keep some good tone in the muscle groups that they use, and this is important in most martial arts.
You could do all kinds of conditioning exercises, like running or swimming or something. If you enjoy doing those things, then go ahead.
When it comes to training, for most of us time is limited and we need to decide how best to utilize the time that we have. If we are training a martial art seriously, we may find that there is not extra time for running, swimming, or weightlifting. So, what do we do?
If you train your martial art seriously, I think you will find that it will get you into shape over time. Just keep at it, be consistent and regular, and you will start to see the difference after a while.
The most important thing in my opinion is that you must be doing something that you enjoy, for its own sake. For example, no matter how much you believe weight lifting would be GOOD FOR YOU, if you don't actually enjoy doing it, you will not stick with it.
I got lucky: I found martial arts when I was young, and I have simply enjoyed doing it. I enjoy the simple process of training and practicing, not for goals or rank or something, but just for DOING it. To me, it's fun. And as a very nice addition, my training keeps me in shape.
Like I mentioned, I do a modest amount of situps and pushups, but this kind of thing is definitely a supplement to my martial arts training, and will always take a back seat. At various times, I have incorporated weight lifting, running, and swimming, but again, as boredom sets in, or time gets tight, these things get sacrificed first.
I actually did enjoy running and swimming, but the time issue is a big factor.
Hope this helps and gives you something to think about.