How does prednisone work?

You can also look up T cell activity to get a more molecular definition,

Prednisone belongs to a class of medications called corticosteroids.
Prednisone mimics the action of Cortisol, a natural corticosteroid produced by the adrenal glands.
Prednisone is often prescribed because it suppresses inflammation. It does this by slowing down and stopping the processes in your body that are involved in your inflammatory response. This can reduce the signs and symptoms of inflammatory conditions, such as arthritis and asthma.
For more information see: https://www.drugs.com/prednisone.html

Hello aquanaut,

Prednisone is part of a group of medications called glucocorticoids. These medicines are a type of corticosteroid, or "steroid" for short. Prednisone is similar to glucocorticoids that occur naturally in the body.

Although glucocorticoids have numerous affects in the body, they are used mostly for their anti-inflammatory or immune-suppressing properties. This drug works for most conditions by decreasing inflammation or suppressing an overactive immune system. When prednisone is taken for more than a few weeks, the body becomes accustomed to it and begins to make less of its natural steroids.

https://www.drugs.com/monograph/prednisone.html