Kayaking is not too difficult in calm waters. It can get more difficult in exposed conditions or strong wind. The kind shown in your photo are "sit on top" which are good for beginners and very stable. Others are true kayaks and your legs go inside.
There are two ways you might end up hiring a kayak:-
Off a Resort Beach. Beachfront resorts may have sit on top kayaks for use of their guests (often for free). In this case, there will be very little instruction given. You would be confined to an area directly infront of the beach where they can see you. These are fine if you are only casually interested, but you will not see much more than if you were on the beach yourself.
Dedicated Kayaking Trip. If you are more serious there are companies that will run dedicated full-day or multi-day kayaking trips around Phang Nga bay (the large bay formed by Phuket). These companies will pick you up from Phuket and transfer you out the islands by longtail or speedboat. Then you kayak around with a guide. Instruction would be provided in this case. Best if you tell them you are beginners as it could be awkwards to be on a trip with advanced paddlers. There seems to be a large variation in prices and I suspect you get what you pay for.
I can recommend Paddle Asia (pictured below) if you are after a multi-day trip. There are many, many islands. If the wind comes up at all, you can always stick to the sheltered side.
I would recommend a separate day kayaking rather than trying to combine with a Phi Phi trip. It is a long way from Phuket to Phi Phi; A fast ferry takes an hour and a half. I think it's better to explore an small, unpopulated island by kayak than around touristy Phi Phi.