Describe the various ways in which the plasma membrane permits interactions with the outside environment.

By interacting with the external environment, if you mean how molecules are transported outside and into the cell then there are 3 main ways of transport.

Passive transport which refers to the movement of molecules into the cell without using any energy. This includes osmosis (movement of water), diffusion (movement of small molecules like salt) and facilitated diffusion which is the movement of large molecules such as glucose via by channels on the plasma membrane.

Note, in diffuson the cell wants equilibrium which means that the cell wants the same ratio of a specific type of molecule compared to the external envionrment. In other words, it's like a a very salty cell becoming less salty because the external envionrment is less salty. 

Active transport refers to the movement of molecules against the concentration gradient using energy.

Bulk transport which refers to the movement of molecules that is influenced by the plasma membrane. One of the ways is for the plasma membrane to engulf particles or expel particles. This allows cells to remove waste.
Go look it up on Khan academy.

Allow large amino acids through