Local anesthetics work by reversibly blocking sodium channels in nerve fibers, inhibiting pain signal conduction. They can provide local anesthesia through infiltration of tissues or regional anesthesia through epidural administration. The two main types are esters and amides, with amides being safer and more commonly used. Potential adverse effects include allergy, toxicity from high doses, and methemoglobinemia. Proper administration techniques and monitoring can help prevent complications.