There's no boats between the two as they're on opposite sides of the Thai peninsula... I guess you could go by boat, but it would take a long time!
The hub town is Surat Thani so you'd need to get a ferry to there, then a bus across the Thai peninsula to Krabi . This can be arranged with a through ticket from a travel agent, or you can get the tickets individually as you go, travelling with public transport.
#2 somtam2000 has been a member since 21/1/2004. Location: Indonesia. Posts: 7,788
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I reckon the earliest arrival in Krabi can be got if you catch the night ferry out of Phangan - this leaves around 2200 or 2300, you cut some zzzs on the numbered matress and pillow provided, transport guys are waiting on the pier when you get into Surathani, they shuttle you up to a little travel agent where you hang around for up to an hour sipping coffee while they round up a minibus and then off you go - usually some time around 6am-7am. Takes maybe 3 hours to Krabi from memory. Maybe a bit less.
You can buy each bit separately or travel agents and bungalows on phangan can sell you a combined ferry-minibus ticket which usually includes transport to the pier on Phangan.
Alternatively you can go up to the bus station in Surathani and catch a more comfortable coach.
P.P.Family company run a ferry/bus/ferry combo to Phi Phi, so their office can probably sell you a ticket to Krabi on the way. They leave Phangan at 7am and are on Phi by 3.30 pm which suggests they are in Krabi just after mid day.
I think their office is in Thong Sala, but usually any small travel agent on the island and a lot of bungalows can sell you a ticket.
A small caveat here. There have been lots of complaints of thefts from luggage in the underbus storage area of coaches put on by private travel companies between Krabi and Surathani (and KSR and Surathani) So to be safe don't leave any valuables in your luggage - have them in your carry pack in the cabin.
Or you can get yourself to Thong Sala, catch the first ferry out, and catch a bus from Surathani bus station.
losing_touch has a great ferry timetable for the southern Gulf islands on his Backpacking in Thailand site which could help - http://www.backpackinthailand.com/gulf_ferries.html