Either a tourist minibus (which will be direct) or a government bus/train to Surat Thani then another bus from there to Takua Pa (it will go by the park entrance).
Khao Lak is past Takua Pa coming from Bangkok. I think somtam may have been thinking of Khao Sok. I get them confused all the time.
Nevertheless many of the Phuket buses from take the mountain road past Khao Sok, thur Takua Pa and then down the coast thru Khao Lak.
Or you could catch a Takua Pa bus and change at the big bus station for a local going down the coast thru Lak.
Now SOME of the Bangkok-Phuket buses go via Ranong where they turn and go down the coast thru Takua Pa and then thru Lak. I don't know how to pick these on the timetable but you could lob at Bangkok's southern bus station and ask when the next was leaving. Some of these buses will be overnight which is a great way of saving a night's lodging for the budget traveller.
Most people organise their Similan trips from resorts/bungalows/agents in Lak, but the actual jumping off point is a little further south at Thap Lamu. The Similans National Park booking office is there about a half km from the pier and they will be able to direct you to one of the travel agents selling boat tickets near the pier. From memory the boats tend to leave around 0800-0830.
If you want to go direct from the bus, get them to put you out on the highway near the turn-off for Thap Lamu which is about 4km away. There should be plenty of songthaews and pickups with dive groups etc to wave down for a ride. From memory the junction is about 8-10km south from Khao Lak central - you will know you are passing thru Lak because the highway becomes a 4-6 lane job thru the small business area and then jumps up on a steep winding route over a headland.