There are fundamentally two types of mint marks on US 1981 proof coins. These mint marks are used on all denominations from the Cent to the Dollar. The type 2 coins are more valuable than type 1 so it is helpful to be able to tell the difference.

It takes some practice and attention to detail to be able to distinguish between Type 1 and Type 2 .

The 1981 Type 1 is called 'worn S' (examples below). This is the same mint mark still in use from 1979 Type 2. There is a capital letter 'S' with open space between the top and the center and between the center and the bottom.

The 1981 Type 2 is called 'Flat S'. The basic shape of the Type 2 'S' is the same as the Type 1, but there are two minor differences; 1) The ends of the 'S' shape are more bulbous on the Type 2 than on the Type 1, and 2) the top surface of the 'S' shape furthest away from the surface of the coin is rounded on the Type 1 but flat on the Type 2. An example of the Type 2 is shown below.

The photos above are just examples. There are a variety of shapes for both mint marks, but given this information and some hands on experience you should be able to begin to discriminate between the 1981 Type 1 and Type 2.