You will need:
1. A timing device. Watch, hourglass, etc. Don't count because you will need that for something else. If you have a tandem partner, he/she can count.
2. A gear chart in gain ratio, preferably.
3. A calculator or a head for numbers.
Now start riding. Start your timing device. Count every revolution of the pedals. Multiply that by the gain ratio and you have your distance. Divide the distance by the time and you have speed. Of course, the rapidity with which you calculate your distance and speed will determine the refresh rate.
Oh, and don't try to talk while doing this...you'll lose you place
The nonsmart ass response is to use the mileage signs on the side of the road or the mile maker posts if your state uses them. Or guess.