If you fly to HK by Cathay Pacific you can book through to Xiamen although they will have to change flights as HK to Xiamen is by Dragon Air which belongs to Cathay.
That is quite cheap when it is combined with the London - HK flight and they would offer the same with Canada - Hong Kong flights. You could stop off in HK for a few days before going on to Xiamen for the same cost but you’d better ask.
However if you are flying to HK with another carrier the flight HK to Xiamen will cost lots as it is considered to be an international flight. I learnt this by flying from Shanghai to HK and back on Dragon for an interview to find that the cost was not far off what it cost me to fly from London to Shanghai and back to London.
So what you do to avoid this "super charge" is take the train from HK to Shenzhen and then a taxi to the airport and fly to Xiamen from there.
If you book an air ticket, the earlier you book a flight the cheaper it is.
You will need RMB once you get to Shenzhen and you can buy RMB with HK dollar or other currencies or credit/debit card in Hong Kong if you are going to spend time there. There are plenty of these money exchange places, like Sheung Wan on Hong Kong side where the metro ends as I know where it is. You can also change money in a hotel but they charge too much. You can also change money at Shenzhen Zhan but I would get it in HK if you are stopping off there. There are ATMs at the station on the left as you walk towards the middle of the building.
According to Google the cost of a taxi from the station to the airport is 120 RMB and the bus is 20RMB
There is also a ferry from HK airport to Shenzhen airport but it does not go often and only goes from the airport = another HK$100 to go to the airport if you have gone into HK. More details in the link http://gohongkong.about.com/od/traveltochina/a/TransportShenAi.htm
There is, or used to be, a shuttle bus from the port to the airport presumably included in the ferry price.
Just looked at the gohongkong.about site and it is very old as it still mentions Oasis air that went out of business the year we met. I see the ferry charges are pretty expensive so I would choose the train the Shenzhen and then a taxi - there is a bus from Shenzhen station to the airport but it took my friend Shaodong quite along time to find where it went from and we had to hang about for quite a long time before one appeared = opt for taxi and experience Chinese driving = pretty wild. I always sit in the front as the seat belts in the back are never available as they are under the seat cover. Would be illegal here as we have to wear seat belts
In China most (maybe all) ATMs can be switched to English language certainly that is the case at Shenzhen Zhan, the airport and in Xiamen.
The other problem is that the key pad for entering ones pin number is upside down to the ones we have here - China ones are 789 at the top and ours are 123 at the top - I think I have that correct.
When I get to the airport I look for an HSBC ATM as they allow you to take out 3000 RMB where others restrict you to 2000 - some guy at Beijing airport told me that other wise I would not have known. This may have changed of course.
We now have new type chips in our cards and when I was last in Xiamen in a super market they could not take my card and when they swiped it the till could not read the black strip - I could not find an ATM in the supermarket so I had to go out and find a bank. All our supermarkets have ATMs and they are easy to find but then they are no as huge as China Supermarkets.
