You gain experience for completing a variety of actions:
-Retrieving a package from a dead drop.
-Spray painting a wall.
-Delivering drugs to your customer.
-Giving free samples to a potential customer.
The experience you gain is also affected by how many points you have invested into the "Quick Learner" skill. The higher your investment into this skill, the more experience you gain from completing tasks. Although currently a visual bug causes this experience not to be added to the total gained in the "Experience Gained" readout, the game still tallies this extra experience in with the total gained.
*Note that performing some actions at night will also provide an experience boost to your actions.