The way that most visitors come to Kagawa Prefecture is one of three ways: by air, by train, or by ferry.
The Takamatsu airport is not so big, but it is clean and very well organized. Not so far from the city it has easy access to the city centre. First off here is the link for the airport itself: https://www.takamatsu-airport.com/en/
Once you arrive at the airport you will likely be going to the city centre to get to your hotel or lodging. There are a few options for you.
The most economical is the Limousine Bus service. The bus departures are in a timely manner to catch visitors getting off of airplanes. You should be okay to catch the bus. When you exit the baggage claim area there is an Information desk right in front of you. Ask them about the bus to Takamatsu Station and they will get your sorted. If your flight is delayed, the bus will adjust its departure time accordingly. How nice is that?
If you are staying at the Hotel Clement you will be taken directly there as it is next to Takamatsu Station. If your hotel is on the main street of Takamatsu (Chuo Dori) the bus makes stops along the way so just let the drive know what hotel you are going to and they will get you close to it. If you are not sure where your hotel is, but have an address in hand just take the bus all the way to Takamatsu station. From there you can pop in a taxi and for minimal fare (if you are in the city) they will get you to the door of your accommodations.
I have heard people express concern about bad mannered taxi drivers and I can only say that from my experience of 20 years I haven’t met a crooked cabbie yet. In fact, they often go the extra mile and take extra care to make sure you get to where you need to go. One time I had a taxi driver chase me on foot for two blocks after dropping me off because he forgot to return a 100 yen coin. I am not sure if I would ever see that in Canada.
Here is the website for the Kotoden Airport Limousine bus. Really the easiest way to get to the city centre: airport bus http://www.kotoden.co.jp/publichtm/bus/limousine/index-en.html
If you are going to Kotohira town, that will need a bus going in a different direction. It does not run as frequently, so please let the Information desk people know where you are going and ask for the Kinku Bus. Here is their website. I am sorry but it is not in English. Show the Information desk staff what you are looking for and they will help you out. https://kinkuubus.jimdo.com
If you are taking a taxi, the ride should be about 30 minutes. Taxi quote I have to date is about 5,000 yen, but that seems a little high. If you are in a rush, or you arrive at an odd hour this may be your only option.
Takamatsu is branching its reach out more and more these past few years. More flights are coming directly to Takamatsu from Seoul, Shanghai, Hong Kong, and Taipei. It’s just great! I’m very curious to hear what attracted people to come to Takamatsu, and also very interested in the kinds of activities or sights people enjoy most. If you have some feedback, please let me know at firstname.lastname@example.org . I would love to hear from you. Welcome to Kagawa!!!