How to tell Eclipse to show content assist automatically?

Go to, Window >> Preferences >> Java >> Editor >> Content Assist >> Auto activation triggers for Java, and enter .abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ , this will trigger the auto activation for class names, methods, etc.

Look in Preferences in Java / Editor / Content Assist and check the Enable auto activation check box is ticked and has a sensible delay.