Encirclement has been used throughout the centuries by military leaders, including famous generals such as Alexander the Great, Hannibal, Sun Tzu, Wallenstein, Napoleon, von Rundstedt, Zhukov, and Patton.
The main form of encircling (the "double pincer") is executed by attacks on the flanks of a Battle, where the mobile forces of the era (Light infantry, Cavalry, tanks, APC's) attempt to force a breakthrough to utilize their speed to join behind the back of the enemy force, and complete the "ring", while the main enemy force is stalled by probing attacks. The encirclement of the German Sixth Army at Stalingrad is a typical example of this.
If there is a natural obstacle (sea, mountains, etc) on one side of the battlefield, only one pincer is needed ("single pincer"), because the function of the second arm is taken over by the natural obstacle. The German attack into the lowlands of France in 1940 is a typical example of this.
A third and more rare type of encirclement can ensue from a Breakthrough in the centre of the enemy front, and exploiting that with mobile forces, diverging in two directions behind the enemy line. Full encirclement rarely follows this, but the threat of it severely hampers the defender's options. By the extreme difficulty of this operation, it can only be executed if the offensive force has a vast superiority, either in technology, organizations, or sheer numbers. The Barbarossa campaign of 1941 saw some examples of this.
A special kind of encirclement is the Siege. In this case, the encircled force voluntarily allows this to happen at a Stronghold location where long-lasting supplies and defensive constructions or fortifications are in place, allowing them to repel attacks. Sieges were particularly common in the Middle Ages, but they have taken place in almost all other eras as well.