Secure both the magnet and reed switch to your bike wheel with electrical tape (either wheel is fine). As shown in the images above, the magnet connects to one of the tire spokes and the reed switch connects to the frame of the bike. This way, each time the bike wheel turns the magnet moves past the switch. Connect the leads form the reed switch to the long wires from your protoboard (orientation does not matter here- it's just a switch)
Use the code below to test your reed switch. When the magnet on the wheel moves past the switch, the arduino should print ~1023, otherwise it will print ~0. Open the serial monitor (Tools>>Serial Monitor) in Arduino IDE to test for your own setup. If the magnet does not seem to be affecting the reed switch, try repositioning it or even adding a stronger magnet if you have one.