File allocation methods determine how files are stored on disk. Contiguous allocation stores all file blocks in one continuous space, requiring a large free block but allowing fast sequential access. Linked allocation stores file blocks scattered anywhere on disk, linking them with pointers, which allows flexible storage but slower access as pointers are followed. Indexed allocation uses a special index block that holds pointers to all file blocks, enabling fast random access even if blocks are scattered. The execution flow starts with choosing a method, then allocating blocks accordingly, and finally accessing the file using the method's approach. Variables like free space and file blocks change as allocation proceeds. Key points include contiguous needing large free space, linked allowing scattered storage via pointers, and indexed providing fast access via an index block.