Drip irrigation is recommended for growing plants in a high tunnel over overhead irrigation. Drip irrigation applies water directly to plant roots through a system of drip tape, filters, and timers, ensuring an even supply of water. It has advantages like improved disease control and efficiency compared to overhead irrigation, which can leave foliage damp and lead to fungal issues. The document also provides instructions and diagrams for assembling different components of a drip irrigation system like headers, tubing, connectors, and ends.