External Pickups
There are many ukuleles that come with pickups already installed. If you want to amplify your acoustic ukulele, then an external pickup is the simplest solution.
They don't require any installation at all. You just attach them to your ukulele and you're away. Usually they will be stuck on with instrument adhesive which promises not leave any mark.
You don't need to buy a dedicated ukulele pickup. A guitar pick up should work fine on a ukulele.
The most respected brands of external pick-ups are Dean Markley and Piezo.
