Tumbling and gymnastics. Seriously. Work on shoulder rolls, cartwheels, round-offs, walking on your hands, handstand push-ups, ring dips, iron crosses, whatever. I've been doing basic tumbling and I've just started to incorporate some work with those gymnastic rings. (Basic stuff; mainly pull-ups, muscle-ups, and ring dips) Your balance, coordination, kinesthetic awareness, and strength will all improve.
Also shrimping, stand-ups, sidemount escapes, neck bridges, bridges, sprawls, penetration steps, and matador guard passes on the heavy bag will all help. Abdominal work will help with your guard game, and no I don't mean a million crunches. Do variations of leg lifts, flutter kicks, etc.
Try getting your heart rate up real high by doing lots of sprawls and penetration steps. When you feel like you're really sucking wind, get in a sprawl position, but rest all your weight through your chest on a heavy bag, so it compresses your lungs. You can also lie on your back and bring your legs over your head. This will get you used to being tired and out of breath and then stuck in uncomfortable positions. Your ability to relax in situations like this makes a big difference in how well you do.
You can make yourself a grappling dummy for pretty cheap, and just practice moves over and over on it. You can't really do much guard/bottom work, but it's great for leglocks and submissions from the top.
Weight training, of course, will make a big difference. Look in the strength and power discussion for tips. You can use weights either to build strength and raw power, or you can do hardcore circuit-type workouts to increase your lactic acid endurance and anaerobic endurance. I suggest a combination of both.
Studying instructionals and fights works big time. I can't tell you how much it's helped me to either watch an instructional video, or constantly rewind parts of a fight to see how someone set up a submission, sweep, KO combination, or whatever. You don't necessarily need to look for instructionals with lots of crazy new moves. If you're an advanced level grappler, start looking at those moves, but if not, just find good instruction on the basics. An example is the basic knee-in-butt guard break. I never used to get this, and people in the gym struggle with it. After watching instructionals, and reading about the move on the internet, I made a mental note of all little parts of the move. Now, when I use this move in the gym, I can break open the guards of the guys on the fight team.
Put all those together and you shouldn't have much trouble figuring out what to do when you're not on the mat. And hey, everyone wants to just roll when they get in the gym. Don't get me wrong, it will make you improve real fast, but you gotta drill, too. Rolling's much more fun, but drilling moves and different areas of the game will make you better. Try to include both in a training session.