If you want to travel from KL to Langkawi Island overland via Kuala Perlis, the first step of your journey is to travel from Kuala Lumpur to Kuala Perlis Jetty.
The distance from KL to Kuala Perlis Jetty is approximately 475 km. So, if you don't want a long overland journey, you should think about maybe taking a flight from either KUL or SZB airports, direct to Langkawi Airport (LGK).
Taking the train is a good choice as you will be able to get to the jetty relatively quickly and train travel in Malaysia is quite comfortable and safer than travel by bus / coach.
To travel from KL to Kuala Perlis Jetty by train you can take one of the fast Electric Train Services (ETS for short) from either KL Sentral Railway Station or from the old Moorish Kuala Lumpur Railway Station.
Travelling by train, you will have to take an ETS service to Arau (the nearest railway station to K. Perlis).
Once you arrive in Arau, the distance from the KTM Arau Train Station to Kuala Perlis Jetty is approximately 18 km.
A taxi from the station to the jetty costs around 25 RM (there is a taxi price list on a notice board just by the entrance to the station).
If you are on a budget, you can take a MYBas bus from the Arau Station to Kuala Perlis, but it is quite slow and you have to change buses in Kangar.
For more information, timetables and fares for the MYBas bus services from Arau to Kangar to Kuala Perlis:
Cheaper than the train, but quite a bit slower, a bus can take you directly from Kuala Lumpur to Kuala Perlis Bus Terminal.
The bus terminal in Kuala Perlis is located just behind a row of buildings that are in front of the ferry terminal (so it is just a few minutes walk to catch a boat).
These days, most buses from KL to Kuala Perlis leave from TBS Bus Station (Terminal Bersepadu Selatan), but you can still find a few other companies that operate from other departure points such as Hentian Duta.
If you have your own vehicle or a rental car, you can now take it over to Langkawi Island from Kuala Perlis.
There are a couple of ferry boat operators that now have regular car ferry services over to the island from Kuala Perlis.