How does the extra dopamine released during drug use affect the brain?

It can increase the brain's reactions to natural levels of dopamine and

It can cause the user to feel more pleasure from normal activities.

Dopamine is a neurotransmitter that is related to the positive feedback/reward system of mammal brains. Higher amounts of dopamine released in response to any stimulation will result in a stronger desire to recreate that stimulus. One could say that the extra dopamine released during drug use causes the brain to desire using the drug again to receive that same pleasurable reward sensation.