The following is the usual way to kanazawa after going out from the custom section.
Follow the sign 'Train or Railway'. Then you can reach the entrance of train station. There are two railways from the airport, JR (Japan Railway) and Nankai. Choose JR line. The ticket office of JR line is just in front of the entrance. There are three kinds of tickets: One is for a normal ticket and the other two are for express service (Kwansai-ShinOsaka and ShinOsaka to Kanazawa) . The price from Kwansai Airport to Kanazawa is 5,670Yen (Former) plus 4480 Yen (the latter). Totally 10,150 Yen for one adult, one way. The tickets for express have two options: reserved seat or non-reserved seat (a little cheaper). When buying the reserved one, you should say about smoking or non-smoking. Each car is smoking or non-smoking. Every train has two or three cars for non-reserved seats. Hence there is sometimes only one non-smoking non-reserved-seat car. I recommend to buy the ticket for reserved seat.
The JR train from Kwansai Airport to ShinOsaka has a common petname Haruka. It goes to Kyoto via ShinOsaka. You can change the train at ShinOsaka or Kyoto to Kanazawa. But the way of change is simpler at ShinOsaka, because the train arrive at No.11 platform of ShinOsaka and the train to Kanazawa starts at the same platform No.11 of ShinOsaka. You need not move with heavy baggages. The train to Kanazawa has a petname Raicho, or Super Raicho (faster) or Thunderbird (fastest) or Hakucho. Raicho is a japanese name of thunderbird. But ShinOsaka is not the last stop of the train 'Haruka' from Kwansai. If you fail to get off at ShinOsaka, then you can change at the final stop of Kyoto. But you have to move from No.30 platform to No.1 platform which is located on the same platform but the opposite side. (about 3-5 minutes walk). The following is the time schedule of both 'Haruka' and 'Raicho or Thunderbird' which have a good connection.