Arriving Osaka airport going to Kyoto?

My elderly aunt and daughter will be arriving Osaka airport at 05:20 Nov. 12. Can anyone please give me detailed information as to how or what train to get to Kyoto after arrival. Is the train station at or near the airport? Any help will be greatly appreciated.

Osaka airport at 05:20 Nov. 12.

I think you mean Kansai airport in the early morning.

http://www.kansai-airport.or.jp/en/index.asp

There is another airport in Osaka, which is Osaka International Airport or Itami Airport which is a domestic airport.

http://www.osaka-airport.co.jp/en/

If you want to go to Kyoto, the easiest way would be taking JR train (Haruka Limited Express). Of course there is a train station just next to the airport. Alternatively you can take a direct bus to Kyoto.

http://www.kansai-airport.or.jp/en/access/index.html

There are many types of discount tickets

http://www.kansai-airport.or.jp/en/otoku-access/index.html

among them the most popular one is ICOCA & Haruka ticket.

http://www.westjr.co.jp/global/en/ticket/icoca-haruka/

Thank you very much. I have forwarded this info to my daughter and this is the best I think. Better to buy online or the price will not differ as buying it on the day of? Thank you very much again for all your help.

You can buy ICOCA and HARUKA ticket on the day of your arrival. No price difference.

https://www.westjr.co.jp/global/en/howto/guide/#ticket-office

Thank you very much. They will do this then, arriving via Jetstar at Kansai airport.

buses is more easier for strangers than trains. It goes directly to JR Kyoto station with no stopping. no ambiguity.
all you need to do is that you ask the bus driver by one word,"Kyoto ?", when you ride.