There are some good bike speed trackers out there, but if you dont want those then here is what you do.
Ride your bike a kilometre, and record how long it takes. Then, take this time, say it was 2.5 minutes (2:30 mins) and find out how many seconds are in it. In this case 160. Now take this speed and divide 1000 by it. It should he about 6.25. Then take this speed and multiply by 60, This is how many m/s you are going at. This is about 22 km/h, or 15 mph. Of course, this is a faily slow speed, usually it is about 30-40 km/h on a mountain/road bike. You can get a more accurate result if you go for 10-20 kilometres, though. You can do this over 10 metres or so while you are riding to find out to. Going down a hill you can get up to about 60 km/h, about 35 mph!
Hope i helped!