Most modern cars have synchros, which allows the collar (the thing that connects the gear to the driveshaft) and the gear to make frictional contact before the dog teeth make contact. This allows the gear and the collar to synchronize their speeds before the gear engages, thus allowing for a smooth shift into the next gear.

However, on cars that don't have synchros, you have to have a way to get the collar spinning at the same speed as the gear. So, you double-clutch it. When you are double clutching, you push the clutch in to dis-engage the engine from the tranny, and you put it in nuetral. Then you release the clutch, and rev the engine to the rpm value at which the engine should be running in the next gear. Then you push the clutch in and put it into gear. Every time you do this, you push the clutch down twice, hence the name "double-clutching".