The minimal proxy pattern involves deploying one implementation contract with full logic. Then, small proxy contracts are deployed that forward calls to this implementation using delegatecall. Delegatecall runs the implementation code but uses the proxy's storage, so state changes affect the proxy contract. This saves gas because proxies are minimal and share one implementation. When a call is made to the proxy, it forwards the call data to the implementation. If the function exists, it executes and updates proxy storage. If not, fallback or error occurs. Upgrading the implementation requires deploying new proxies pointing to the new implementation address.