I just cleaned my gears, derailleurs, and chain. Lubricated the chain with Teflon dry lube. When will I need to re-lubricate again? Will I hear the chain make sounds? Do I do a visual inspection?
If you hear your chain squeaking you definitely need to re-lubricate it. It's also a good idea to re-lubricate after riding in wet weather since the combination of road grit and water tends to strip away the oil/wax.
For more detailed recommendations, see this question: "How often should I lube my chain?"