Lydia from Build Show demonstrates how to coat a California patch, emphasizing the importance of using a large knife for a smooth finish. She explains the process of applying mud in a thick coat and feathering the edges to prevent flashing. Using a smaller knife can result in laugh lines and uneven patches. Lydia recommends using a larger knife, like an eighth or tenth inch skinning blade for better results. She also discusses the significance of avoiding heavy or goopy coats and demonstrates how to properly feather and sand the patch for a flawless finish.