The most common type of cufflinks are the ones with a rotating bar. Fixing cufflinks with a fixed bar is self-explanatory. Cufflinks with a rotating hinge are preferred because they are easier to attach to the cuffs of the shirt. First unfold the bar so it's completely at right angles to the button, put it through the buttonhole and then turn it 90 degrees again, so it's firmly in place and holds your cuffs together.
Not to be confused with the fact that a pair of cufflinks is always a set, when you buy a cufflink, you will always get a double one. With a double knot however, we mean a certain model of cufflinks. A model where both ends of the bar have the same knot, usually this is a small 'ball', diamond, or small cube. The shape should be such that it still fits through the buttonhole opening, so you won't find a rectangular shape with a double cufflink.
Although silk cufflinks are also available, the silk knot refers to two elastic balls. The material consists of a mix of silk and elastane, the ends are rolled up in a beautiful way to form a ball, the two balls are connected by a short elastic in the middle. The balls should be small enough to fit through the opening of your buttonhole, but big enough so that they don't fall out. A usual size is somewhere between 1 and 2 cm. The silk knot is also sometimes made of polyester. Fortunately, there are other names for the silk cufflink, so that there can be no misunderstanding. Other names include the Turkish knot, bachelor's knot, monkey knot or apple ball knot.