When you come out of KIX customs, take the escalator up to the second floor and walk straight across to the rail station. There are two rail companies, Nankai and JR.
Among you options are to:
1 - Take the JR airport rapid service to Osaka station. I think the Hilton is directly across from the station. This is the direct way to go, and the cheapest.
2 - You could take a JR Haruka to Tennoji and change to JR Loop line to Osaka station.
[This message has been edited by unagi1 (edited 07-19-2001).]