Count pedal revolutions against a clock or watch. Count for 6 seconds and multiply by 10. I try to shoot for a cadence of 90, and gear accordingly. After a short while you'll know what that cadence feels like. Just make sure you count complete revolutions, like every time your right foot passes 6:00.

As far as improving your overall speed, there are all kinds of training methods and tips if you want to maximize your performance. I never got into those much myself because I haven't had any reason to "compete" for 30 years or more. I just push myself every solo ride. Ride at whatever maximum effort you believe you can sustain for the length of the ride. You do that often enough and you'll find your perceived level of effort might stay the same, but you'll be riding faster. When I was younger I used to wonder when training rides would start to get easier - after all, I was getting fitter, wasn't I? The answer is of course that they don't. You just get faster as your fitness improves.