How do plants and animals get nitrogen if not from the atmosphere?

Our atmosphere (air) is comprised of 78% of nitrogen. However, this nitrogen is in its elementary state (N₂) and therefore is quite inactive, so the plants can not use it directly. Changing the elementary nitrogen into more reactive forms (NH₃, NO₂, HNO₃) is occurring through the process called nitrogen fixation. It is happening via two processes.

First one is physical nitrogen fixation. When some type of atmospheric physical energy (lightning bolt, for example) reacts with N₂, it splits it in two very reactive N atoms, enabling them to react with oxygen in order to form NO₂.

Second process is biological nitrogen fixation. It's done by bacteria, special bacteria living in the soil, able to use elementary nitrogen for its metabolical pathways resulting in production of ammonia, which can be used by plants. It's noteworthy that bacteria are responsible for about 90% of all nitrogen fixation.