Consider your pant length. If you wear your baseball pants cuffed at the ankles, it may not even be worth it to wear stirrups, as only an inch or so worth of stirrup will be exposed, if that. If you wear pants cuffed at the knees or shins, stirrups are appropriate. Lukas recommends pants that come to the mid- to upper shin for the most classic look.
Put on a pair of white socks. Over-the-calf tube socks are your best bet, as they have to rise high enough to prevent any skin from showing through the openings in the stirrups. Crew socks will be too short. The newer the socks, the better, because you need strong elastic at the top to hold the sock in place. Any sagging in your white "sanis" can cause the stirrups to sag as well, and that can create a tripping hazard.
Put the stirrups on over the white socks. Stirrups are essentially colored sleeves that cover the lower leg with a skinny loop that goes around the bottom of the foot. (See the link in the Resources for examples.) The loop should be aligned so that it comes up the sides of the leg, roughly over the "knobs" on either side of your ankle. How high you wear the stirrups is as much a matter of personal preference as the length of your pants. Some players prefer to have only the narrow parts of the loop visible between their pant cuffs and shoes. Others like to have some of the sleeve visible, too. Either way, the stirrups should be pulled up under the pants. Nothing looks sillier than a strip of bare leg between your baseball socks and baseball pants.
Make sure the sleeves of your stirrups are gripping your leg firmly. This is a safety issue. When stirrups lose their elasticity, they sag. As the sleeve sags down the leg, the sides of the loop go slack and stick out. A player's cleats can easily get caught in the loop, causing him to trip and fall.