My cardio has long been my downfall, owing in part to being on very high doses of prednisone for a long period of time (take home warning to guys who like steroids, anabolic or otherwise: that shit will mangle your heart; even if it's just an anti-inflammatory to treat disease.). I've had to work a lot to get my cardio up and I have had plenty of health setbacks that have made me have to start all over again (you lose cardio fast and it's hard to get back). As a respiratory therapist, I have a particular interest in cardiovascular stuff in general and cardio training specifically.
There are really three aspects to what we mean by "cardio" and there are different approaches to how best to train each one. First is your anerobic threshold. That's basically how long your muscles are able to go before using up the available oxygen and changing to anaerobic metabolism. Once a muscle goes into anaerobic metabolism it will quickly use up energy faster than it can be replaced and the muscle fails. Second is your aerobic conditioning which is the efficiency with which your cardiovascular system delivers oxygen rich blood and removes waste. Last is your recovery time. Different trainers and physiologists have different ideas about how best to train those aspects, but the end result is the same; you need to work on all three areas or your athletic endurance will suffer.
To train your anaerobic threshold, most trainers will have you do some form of intervals or other high-intensity exercise. The important thing is to use large muscle groups and train well into "the burn" of anerobic metabolism (sometimes called "training to failure" but I don't care for that misnomer; rarely do you ever actualyl get to total muscle failure. Usually your mind gives up on you first and you quit when it just hurts too much) or do intervals such as sprints. Another way to train anaerobic conditioning is with static strength training -- typically a HARD isometric contraction that elevates the heart rate for a proscribed period of time (e.g. clinching a medicine ball for time, holding up a leg press at your 1-3 rep max weight for time, etc). What this does is stimulate the production of myoglobin and improve mitochondrial efficiency within the muscles. This means they can go longer before switching over to anerobic metabolism. Once a week is plenty to train your anaerobic threshold. You need rest and recovery to prevent over-training. EDIT: note that this is not the same as a typical anaerobic weightlifting routine. You should be using large muscles especially in combination and training to near-complete exhaustion. That's why you should only do one of these days a week and REST. If you're doing static contractions (which looks like something Einstein uses in his program for Chuck) it should be borderline torture. If it just hurts a bit, you're not squeezing hard enough. Also, you need to be sure it's a full body workout if you want your grappling endurance to improve. When I was rock climbing regularly we'd do dead-hangs to failure with our arms at different angles which improved the anaerobic threshold in my forearms but did nothing for my general conditioning. You have to get well into the "burn" zone and elevate your heart rate or you're not stimulating the muscle properly. And once again, REST. You don't improve anything without growth and growth only occurs during rest periods.
To train your aerobic conditioning you need to stay just below the anaerobic threshold. Think of aerobic training like shoveling coal into a boiler or furnace -- too much and it burns to hot and you blow up the boiler. Too little and the boiler cools down and doesn't work. This means keeping your heart rate at a moderate level for a longer period of time (e.g. 60-70% of max HR for 45min-1hr at least). You should still be able to carry on a reasonable conversation during this. If you're too out of breath to talk then you're not training your aerobic conditioning, you're training your anaerobic threshold. This should be at least twice a week. If you're in good shape, plain ol' jogging should get it done but if you really want to maximize your gains, get a heart rate monitor. If you start gettig your heart rate too high during this workout you're back to training your anaerobic threshold and that's going to slow your overall progress.
To train your recovery time you need to improve the efficiency with which you get back below your anaerobic threshold. This one's easy to train: maintain a low-moderate heart rate for a long period of time -- no less than an hour and a half; two is better. This should basically be a brisk walk that gets you to break a mild sweat. This improves the efficiency with which you remove waste products from the muscle by working the right side of the heart (muscle contraction assists venous return; increased venous return increases the work of the right heart which also delivers blood to the lungs). Once or twice a week is plenty as long as you're putting in the time; at least 90min of sustained effort.
Again, unless you're training all three aspects you're not maximizing your endurance gains. There's a lot of decent advice on this thread (and some less than decent). As long as you're working from first principles and training all three areas you'll improve your cardio. Keep in mind, it takes WEEKS to actually improve your VO2-max (the measure of aerobic efficiency) and if you're serious about improving your cardio invest in a good heart rate monitor. Keep at it and know that you're in good company.
Debacle: I kept it under thesis-length. How's that?