Resources: http://www.japan-guide.com/e/e4006.html


So how do I get to Osaka City?
From Kansai International Airport

1)Nankai Raiway
The most popular way would be taking the Nankai Railway to Nankai's Nanba Station. The Limited Express trains cost 1390yen and takes 30mins. The Express trains costs 890yen and takes 45mins.
If your accommodation is not in Nanba, you can walk easily to the Nanba Subway station that's located nearby and take the subway to your destination.

2)Airport Limousine bus
If you have lots of luggage, a good way would be to take the airport limousine bus. It stops and picks up passengers from various Hotels in Osaka, as well as JR Osaka Station, JR Nanba Station and Itami airport.
Charges varies according to stop-off location.
Information about pickup/drop-off locations and charges can be found here.

3) JR lines
For JR pass holders, The Haruka Ltd Express trains stops at JR Tennoji station and JR Shin-Osaka Station. To Tennoji Station it costs 1760yen for an unreserved seat or 2100yen for reserved seat and takes 30mins, to Shin-osaka station it costs 2470yen for an unreserved seat or 2800yen for a reserved seat and takes 50mins.
Not exactly the most cost effective way, but its good if you have the JR pass you can take this to save time..

Another route called the JR Airport Rapid service stops at JR Tennoji Station and JR Osaka station. To Tennoji costs 1030yen and takes 50mins and to Osaka station it takes 70mins and cost 1160yen. From both stations you can take the subway. This route would be the cheapest to both Nanba and Umeda area.


Itami Domestic Airport
Though closer to Osaka city, there isn't exactly a direct train line though the train method is more economical.

via train, From Itami, take the Osaka Monorail to Hotarugaike Station. From here transfer to the Hankyu Railway Takarazuka line to Umeda station. From Umeda you can take the subway to other locations in Osaka. For the first leg it costs 200yen and takes about 2mins (as it's only 1 stop away), the subsequent leg to Umeda costs 220yen and takes 18mins.

Itami has airport bus service as well. Pick ups are available from Osaka Station, Nanba OCAT building, etc. Check out this link for pricing and locations.

Tokyo

1)Shinkansen
This is the most popular option, especially if you have a JR pass. You can board at either JR Tokyo Station or JR Shinagawa station for the Tokaido Shinkansen line.
>> Via nozomi, it takes 155mins and costs 13800yen for a reserved seat and 13500yen for non-reserved seat (Note, not valid for JR pass).
>> Via Hikari, it takes 180mins and costs 13500yen for a reserved seat and 13240yen for non-reserved seat.

2)Highway bus
This is my favourite option.
It's cheap. From 123bus company, it costs 4100yen to 8500yen depending on the type of bus chosen and date of departure.

For JR bus company, tickets can be bought just before departure from JR Tokyo Station (near Minami Yaesu Exit).

Pickup locations are usually at JR Tokyo station, Shinjuku bus station, Disneyland Resort, Ikebukuro or Shinagawa.
Dropoff locations are usually JR Osaka station, JR Nanba station, JR Tennoji station or Universal Studios.

Generally night sleeper buses take about 9-10hrs.

3)Domestic Flights
Will do a writeup on Domestic flights seperately. look out for it.

Narita airport
Read here for method of travel to Tokyo City, and from there you can pick from the 3 methods above for travel from Tokyo to Osaka.

Kyoto
1)JR
JR Kyoto Line connects JR Osaka station to JR Kyoto station and vice versa. Costs 540yen and takes 30mins. Valid on JR pass.

2)Shinkansen
Only if you are on the JR pass, if not it's not worth it.
It takes 15mins and costs 1380yen via Shin-Osaka station using the Kodama or Hikari trains.

3)Hankyu railway
The Hankyu Kyoto line from Karasuma or Kawaramachi Station to Hankyu Umeda stationtakes 40mins and costs about 400yen. Good way if your accommodation in Kyoto is located in that area, and you stay in Umeda area.

4)Keihan raiway
Keihan Main line Ltd Exp from Sanjo Station to Yodoyabashi (somewhere in between Nanba and Umeda on the Midosuji line) takes 50mins and costs 400yen. Good way if your accommodation in Kyoto is in Central Kyoto and you stay in Nanba.