Cufflinks, those most indispensable men's accessories, come in several major varieties. I offer a primer and some suggestions. N.B. My naming conventions are my own and are not likely to be understood by anyone who doesn't read this post.
The Clasp: The Clasp has a little widget on the back that pivots freely; the image above shows the link in its fastened position. If the rotating pin is perpendicular to the "public face" of the cufflink, you can easily line up all four holes of the French cuff and push the pin through, then rotate it to the shown configuration. The public face should point away from your body when your hands are at your sides.
The Good: The Clasp is very secure and is far and away the most common type of cufflink available at most retailers, from Filene's to Brooks Brothers. It also tends to be less expensive than other types.
The Bad: People sometimes see the inside of your wrist, and that means they see a homely cylinder of inexpensive metal.
The Two-Face: The Two-Face has two public faces, usually identical. The faces are held together either by a solid bar, as shown, by a chain, or by a snapping mechanism. Generally, to get a Two-Face on, it's easiest to push the public face through the French-cuff hole from the side, one hole at a time. If your hand can fit through your French cuff when it's fastened, it's even easier to fasten the cuff while your shirt's still on the hanger and then shove your hand through.
The Good: The Two-Face is far more elegant than The Clasp--your inner wrist is just as handsome as the outer.
The Bad: The Clasp is extraordinarily hard to find in most retail stores. Recently, Jos. A. Bank has started to offer simple Two-Faces for a reasonable price. I got the pair shown during one of their "50% off everything" sales. Quite a good deal. The Clasp is also hard to put on when you're in a hurry.
The Monkey's Fist: The Fist (treated more extensively here) is a Two-Face made out of cloth with a knot of string on either end. The versions I've seen are held together by two strands of stretchy fabric. This means you can easily put the link in place while the shirt is still hanging (which means you can use both hands to maneuver it) and then stretch out the cuff opening when you're ready to put the shirt on.
The Good: Inexpensively had at Brooks Brothers. Comes in a huge variety of colors. Easy to put on.
The Bad: Somewhat less formal than a metal link, but depending upon whom you're meeting, that can be an excellent thing.