Three BIG things in Jiu-Jitsu, that I've learned in the 6 months I've been doing it (no gi), are:
1. Move your hips. Use your hips. They're your center of gravity, and if you notice, every move you make from the guard requires you to move your hips in some way. Don't let anyone pin your hips down. A BJJ guy with his hips pinned is equivalent to a wrestler with his shoulders pinned. Your hips should be rotating, exploding, sliding out, etc. You need to coordinate your upper body with your lower body.
2. Wait, think, and then explode. Let's say you're going for a kimura from the guard. You have two options. You can either a) reach up, put your hands in the basic position, muscle it out and hope for the best (which will ultimately lead in you wasting a lot of energy and time), or b) wait, plan the EXACT movements your entire body is going to make, distract him, and then EXPLODE into the move. Trust me. Train repetition of techniques so you can get the form down perfectly, so that you don't need to worry about it so much in a match. I still find myself making the mistake of trying to go all-out, and muscle through submissions. You won't catch anyone good like that. Anyone who is half decent at Jiu-Jitsu knows the setups and knows the moves you're going to do. You need to wait until the right moment, then explode into the move before he can react.
3. Conditioning plays a huge role in how you do. I'm obsessed with MMA. When I get home from school, I train. And then I do homework. Then I go to my MMA gym and train. When I get to the gym, I make myself the last guy there. And I roll with everyone and anyone I can. Guys at my gym now will roll with me when they want a workout, and they're always commenting on my cardio and conditioning. Skill will only get you so far. I'll go with guys who I can't submit in a short match, but if we go for no time limit, I catch them when they're tired, after 20-30 minutes. Just roll constantly, and condition when you're off the mat, and get your cardio up. Fatigue will make the most skilled BJJ student sloppy.
Seriously. Just try all three of these concepts. I'm not saying you'll instantly submit everyone. But they should definitely give you significant improvement.