The PostgreSQL query planner uses Sort nodes to handle sorting operations when an input query has an ORDER BY clause or intermediate resultsets need to be sorted. There are different types of Sort nodes, including the default Sort node, Quicksort, External Merge Sort, Top-N Heap Sort, and Incremental Sort. The choice of sorting method depends on factors such as data size, available memory, and query requirements. Optimizing working memory, selecting only necessary columns, and having appropriate indexes can improve sorting performance in PostgreSQL.