Changing the pressure

Changing the pressure affects the equilibrium only if there are reactants and/or products that are gases. In general, increasing the pressure on an equilibrium mixture causes the reaction to shift to the side containing the fewest number of gas molecules.

In the Haber process, all species are gases, so you do see a pressure effect. Think about the sealed container where your ammonia reaction is occurring. (The reaction has to occur in a sealed container because everything is a gas.) You have nitrogen, hydrogen, and ammonia gases inside. There is pressure in the sealed container, and that pressure is due to the gas molecules hitting the inside walls of the container.

Now suppose that the system is at equilibrium, and you want to increase the pressure. You can do so by making the container smaller (with a piston type of arrangement) or by putting in nonreactive gas, such as neon. You get more collisions on the inside walls of the container, and therefore, you have more pressure. Increasing the pressure stresses the equilibrium; to remove that stress and reestablish the equilibrium,  pressure must be reduced.

Take another look at the Haber reaction and look for some clues on how this may happen.

N_2(g) + 3H_2(g) ↔ 2NH_3(g)

Every time the forward (left-to-right) reaction takes place, four molecules of gas (one nitrogen and three hydrogen) form two molecules of ammonia gas. This reaction reduces the number of molecules of gas in the container. The reverse reaction (right-to-left) takes two ammonia gas molecules and makes four gas molecules (nitrogen and hydrogen). This reaction increases the number of gas molecules in the container.

The equilibrium has been stressed by an increase in pressure; reducing the pressure will relieve the stress. Reducing the number of gas molecules in the container will reduce the pressure (fewer collisions on the inside walls of the container), so the forward (left-to-right) reaction is favored because four gas molecules are consumed and only two are formed. As a result of the forward reaction, more ammonia is produced!