There's a distinction in the naming of classes of motorcycles, depending on their use: racing, hill climb, dragsters and so forth are one class; your ordinary here and there machine (to take you from here to there and back again) is commonly called a cruising bike (or "cruisers"). It's these that we are concerned with here.
Most cruisers are sold "naked" — i.e., sans windshield. Most makers have their own set of add-ons, which of course are guaranteed to fit; there are many, many aftermarket sellers for all the makes; and there are "universal" windshields which typically attach to the handlebars and are adjustable.
Motorcycle windshields serve the same purposes as on any other vehicles: projectile defense and air deflection. The latter is far more important than for any other form of vehicle; the airflow at high speeds is very powerful and over any extended period can cause acute pain in the skin and in the skull, not to mention temporary hearing loss; even if you're wearing a helmet, the turbulence at speed can cause severe headaches. Only the very toughest riders will undertake trips of any length without some sort of windshield!
Most of the kits available for your particular putt attach to the frame and the forks rather than to the handlebars. Mounting brackets may or may not be supplied with the kit — ask before you buy! If you're buying a used windshield, insist that it be installed for you. Care has to be taken when installing windshields not to pinch any control cables or wiring or brake lines; check this before doing the final tightening. Likewise, the controls must not be impeded by the new windshield, and your mirrors must be able to give you the correct vision in every direction after installation: if the windshield goes behind a mirror, then it's the wrong one — or you need new mirror mountings.
The windshield's material is of great importance. It must be clear and not prone to ripples or distortion at the edges or on the curvature: it must be durable, so that cracks don't develop around the edges; and it must not be subject to color changes which would impede your vision. Windshields are commonly made of Lexan (polycarbonate) or Lucite (acrylic). There are differences but it seems that it's a matter of choice from experience.
Once the windshield is chosen and mounted, a crucial adjustment remains: that of height. It's supposed to protect you from missiles and bugs and atmospheric conditions, but if it should become iced up or really opaque with junk, or if fog conditions cause windshield glare, you have to be able to see over it. It's supposed to protect you from the airflow; but if you're driving in hot climates and the windshield diverts ALL the air, you will be driving in a furnace! Contrariwise, if it diverts too little, you and your passenger are going to suffer from turbulence, and all the problems that causes. Ideally, you should be able to see over the windshield for normal driving but be able to tip your head so as to bring your eyes below its edge for comfort. When looking though the windshield you should be able to see far enough ahead for reaction time — typically about a hundred feet, or four seconds' driving time.
The consensus seems to be that the top of the windshield should be just below your level vision line while you're in your normal driving posture — some say, more precisely, about at moustache level. Note that this is without significant rake — that it must be fairly vertical as otherwise you're setting up a fierce slipstream directly into your eyes. You can cut out cardboard dummies of various heights and get an idea of the correct setting. Obviously you have to test-drive it before you make the final installation. And bear in mind that the handling characteristics of the bike are going to be changed by the existence of the windshield, so take it easy until you understand and are comfortable with the differences.
Motorcycle windshields can be repaired — some acrylic manufacturers offer repair kits — but if it's more than a scratch, you have to consider whether the integrity and strength of the windshield are too seriously compromised to remain safe.