Drip irrigation and sprinkler irrigation are two common irrigation methods discussed in the document, with drip irrigation applying small quantities of water directly to plant roots through a network of pipes and emitters, while sprinkler irrigation sprays water into the air to fall on soil surfaces resembling rainfall using pumped water and sprinkler heads. The document outlines the components, operation, advantages, and limitations of each system along with their suitability for different crop types and soil conditions.