To learn how Java implements collections, the definitive place to go is the source code itself, freely available. Generally, Lists are implemented as either arrays (ArrayList) or linked lists (LinkedList); sets are either hashtables (HashSet) or trees (TreeSet); and maps are hashtables (HashMap).
Algorithms for manipulating arrays, linked lists, hashtables, and binary or n-ary trees (add, remove, search, sort) are complex enough in themselves that an entire course is necessary to cover them all. Anyone doing their own program design typically needs to understand these algorithms and their performance tradeoffs by heart. There's no substitute here for textbook study and/or practice.