By bus or minivan
Regular buses and shared minivans run from Hat Yai Bus Station to Krabi's bus terminal, covering the roughly 200km route in about 4 hours by minivan or a little longer by standard bus, with several departures a day. This is the standard way to make the trip, and reasonably priced (fares typically 270-650 THB depending on operator and class).
By private taxi
A private taxi covers the same route in around 4 hours, at a higher fixed cost — worth it for groups splitting the fare or anyone wanting to skip a shared van's other stops.
Why no flight or train
Krabi isn't connected to Thailand's rail network, and there's no direct flight between Hat Yai and Krabi — despite both having their own airports, the route simply isn't commercially served, likely because the direct road journey is already fast enough to make flying unnecessary.
Why travellers make this trip
Hat Yai is a common overland entry point from Malaysia and Singapore by road or rail, so this route is mostly used by travellers arriving from further south rather than a typical domestic Thailand connection.