The advantages of taking this route are that the ferry crossing is the shortest possible route from the Malaysian mainland to Langkawi Island (the long ferry crossing from Georgetown to Langkawi can often make people seasick in rough weather) and it can be much less expensive travelling this way.
You can take a quick and cheap KTM Komuter (commuter) train from Butterworth Railway Station to Arau Railway Station.
Once at Arau, you can then take a taxi (or Grab car) to get to the Kuala Perlis Jetty (taxi's cost around 25 - 30 RM).
There is also a cheap local bus that can get you from Arau Station to Kuala Perlis Jetty, but it takes a long time and you will first have to take the bus from Arau to Kangar, then change to another bus from Kangar to Kuala Perlis.
If you want to learn more about this "MyBas" service from Arau Train Station:
If you want to take the most direct way to get from Penang Island to Kuala Perlis, there are a number of bus companies that operate coaches to Kuala Perlis from either Sungai Nibong Bus Terminal on the island or Butterworth Bus Terminal (Penang Sentral) on the mainland.
The only trouble with these buses is that you will have to book your seats well in advance as they are nearly always full (all these buses originate from places like Kuala Lumpur and the route to Kuala Perlis / Langkawi is extremely popular).
If you turn up at the bus station on the day of travel and try and buy a ticket to Kuala Perlis it is usually impossible to get a ticket!
Driving from Penang to Kuala Perlis gives you the chance to take your car over to Langkawi Island as this is where you will find departures for the only car ferry services to Langkawi.
The distance from Georgetown, Penang to Kuala Perlis by road is around 180 km (if you use the toll roads/highway)
If you don't want to take your car over to the island, there are plenty of places near the ferry terminal that offer parking services for around 10 RM per day.