Following instructions provided by Piaggio, the Vespa scooter's manufacturer, most people can install a speedometer (speedo) cable with a little bit of work. It just takes a bit of patience and understanding how to coax a new cable through the fork and to sit in place. Once the cable is installed, the speedo gear in the wheel hub and the speedometer do all the rest of the work as the front wheel spins.
Identify the model and name of the Vespa scooter you have. Provide this information to a Vespa parts shop when purchasing a new speedometer (speedo) inner cable and outer house, if needed. Obtain the cable assembly and purchase some automotive grease and shoptowels at a local auto parts store.
Place the scooter in the clean work area and remove any accessories such as windshields from the headset area (the frame that holds the headlight). Use a screwdriver and loosen the headset top. Lean down and identify the speedo cable leading into the front wheel hub. Pull it out of the wheel hub (it should just be snug but not stuck) and push it into the front wheel.
Using the slack created by pushing up on the speedo cable, pull on the headset top gently as it lifts from the headset frame. Disconnect electrical connections as needed. Pull the headset top far enough until you can reach the speedo cable (the one going into the speedometer from the bottom). Grab the speedo cable housing and pull a few inches up to gain clearance from the rest of the headset.
Reach under the speedometer where the old speedo cable inserts. Unscrew the holding washer until it is totally loose. Pull the cable housing off the speedometer bottom and put aside the disconnected headset top. Pull the inner cable out of the exposed cable housing and discard. Examine the cable housing to make sure it doesn't need replacement. Look for holes, kinks, or tears in the housing.
Take the new inner speedo cable purchase and grease it. Use your hand and a dollop of grease. Rub it down the entirety of the new cable. Carefully insert the bottom end into the top of the outer cable housing still sticking out of the headset bottom (install a new housing if needed first). Unstick the cable entry by pulling the bottom of the housing through the fork an inch or two when the inner cable gets stuck in a curve. Make sure the inner cable is entirely inserted when done except for a small end stick out of the top of the housing.
Grab the headset top and line up the bottom of the speedometer with the top of the speedo cable housing. Take the securing washer and screw it onto the bottom of the speedometer after inserting the housing. Secure the washer tightly but do not overtighten.
Gently pull the speedo cable housing back down through the fork tube while lowering the now attached headset top back to the headset frame. Reconnect all electrical switches as needed. Pull the system down until the headset top is seated on the headset bottom frame. Resecure the top with a screwdriver and the screws put aside. Reconnect the bottom of the speedo cable and housing to the front wheel hub where it originally came out.
Make sure to grease the cable when installing as this makes the installation very easy. When it does get stuck going in, just move the housing within the front fork tube to get it past the friction point.
Don't just assume any speedo cable will work for your Vespa scooter. Different Vespa models were designed with different-sized cables. They vary in length and thickness and in securing parts. The speedometers themselves also vary over time as well. Follow the instructions or you will needlessly buy the wrong part and waste your time and money.