Now, considered you are living at any state which South of Perak. You can just go to Bus station to buy a ticket to Alor Setar.
The direction should be: Alor Setar -> Kuala Kedah -> Langkawi.
The actual route I have been through (Ipoh -> Butterworth -> Alor Setar -> Kuala kedah or Kuala perlis) used me 11 hours to reach Langkawi.
Kuala Kedah is the terminal where you get Jetty to Langkawi. But be carefull at this point - Kuala Kedah, here have agents (cheaters) who will introduce hotels, car rentals and special tours for you and please don't ever believe them! I tried and I totally regretfull. Just rent a car when you arrived Langkawi and I pretty sure you can get a fine hotel there.
Recommended ( City Bay view, Citin Hotel, Budget Inn, and Continent Hotel) All around RM90-RM165.
Okay. Tips over. Enjoy and don't forget explore with a map!
Map - Get there for free as well as you arrived Langkawi.