Originally Posted by Carbonfiberboy

Mashing is easier on your aerobic system, but harder on your legs. Spinning is the opposite. Spinning is the way to go because your aerobic system won't wear out on a ride, but your legs will. So until your aerobic system comes up to speed, you may actually go a little slower when you spin than when you mash. Ignore that and just stick with it. Do get a cyclocomputer with cadence. They're not expensive, expect $30-$50.

The quickest way to improve your spin is to spin much faster than is comfortable. This is neuro-muscular training which teaches your nerves and muscles when to fire. There are two types of drills. The first is easier, but I of course prefer the second:
1) Spin-ups - Increase your cadence to the point where you begin to bounce in the saddle. Hold that for 1-2 minutes, then recover at normal cadence for 5 minutes and repeat until whenever.
2) FastPedal - Increase your cadence, in a very low gear, to a point where you begin to bounce in the saddle or 115-120, whichever comes first. Hold that cadence for 15 minutes. Over a period of weeks, gradually increase the length of time at high cadence until you can do 45 minutes of continuous high cadence pedalling. As the length of the interval increases, you will find that your cadence will increase also. Do this drill once/week.

Personal preference: I like 88-94 on the flat, 78-85 climbing if I have a low enough gear to allow that cadence.

When doing this, keep your feet flat and imagine that you have a layer of air between your foot and the sole of the shoe. IOW, don't push down! Keep your back straight and use a low enough gear that your breathing stays relatively slow and easy. These drills are much easier to do on a trainer or rollers than on the road. However, they must be done on your road bike, not a gym stationary or spin bike.

These drills are in addition to, not replacing, the advice given above.