How do organisms adapt to their environment?

Natural selection. When there's a change in the environment, species develop certain characteristics so they can survive better in these environments and pass on these characteristics to their offspring. That is they how adapt to the environment.

Homeostasis - regulation of internal system

Organisms adapt using natural selection. For example an animal in a hot environment may sweat more, or evolve to grow bigger to increase it's surface area, and therefore evaporate more water/lose heat in order to maintain its body temperature. These physical aspects change over time allowing organisms to fit to a certain environment.