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At Haneda airport: 
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When you finished immigration and baggage claim (You need to take your baggages in Haneda airport  not Itami !  ) and went out the Exit, just go and keep walking to the right. 
Then you can find a domestic flight check-in desk. 
After you hand over the baggages,  take an elevator which is again in the right of the check-in desk and move to the stop for free shuttle bus between terminals. 
If there is no enough time to transit to the domestic flight and there is a long queue, just ask a help to the staffs. They are very kind and will help you.   

The terminal you arrived is Terminal 3(International airport terminal), so you need to move to the domestic terminal (JAL is Terminal 1 and ANA is Terminal 2). 
You need a security check again in the domestic flight terminal and that’s all. 

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At the Itami airport, 
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You need to buy the bus ticket before. 
And this site will precisely let you know. 
https://www.okkbus.co.jp/en/busstop/itm/

You can use the credit card for the ticket vending machine in Itami airport  
or  buy the tickets directly in the ticket office of the airport. 


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At the Kyoto Station
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If you arrive at Kyoto Station by airport shuttle, you can find a taxi station very easily. 

If you arrive at Kyoto Station by Shinkansen, Please go out the center exit [中央出口] of Shinkansen in Kyoto station→ Walk to the left 20 meters and find an escalator in the right side to go down the stairs → Taxi station is just there. 
 

Then, take a taxi and show your hotel address.