Kansai International Airport: There is no Yoshino airport transfer worth hunting for. Take the JR Kansai Airport Rapid to Tennōji (about 45–55 min), walk through the connected Tennōji/Osaka-Abenobashi complex, then take the Kintetsu Minami-Osaka/Yoshino Line to Yoshino. Allow roughly 2½–3 hours total and about ¥2,300 on ordinary trains; use the limited express for the final leg if the timetable suits you.
Osaka Itami Airport: Take the airport limousine bus to Tennōji, then walk to Osaka-Abenobashi and board the Kintetsu Yoshino Line. The bus is around 30–40 minutes; the train is 75–90 minutes, so plan on about 2¼ hours door to door and roughly ¥1,900–2,400. A taxi all the way is a bad use of money.
Osaka-Abenobashi Station (Tennōji): This is the cleanest Osaka gateway. Kintetsu rapid-express trains run directly to Yoshino in about 90 minutes for ¥1,170. A direct limited express cuts it to about 75 minutes; total fare is about ¥1,690. Reserve the limited express on spring weekends, but do not pay for it merely to save a few minutes if the rapid-express leaves first.
Kyoto Station: Use Kintetsu, changing at Kashihara-jingū-mae for the Yoshino Line. Expect around two hours, depending on the connection, and roughly ¥1,500–2,000. It is straightforward but not a day-trip commute: leaving Kyoto after mid-morning makes Yoshinoyama feel rushed.
Kintetsu Yoshino Station: This is the railhead, not the ridge-top temple town. Walk a few minutes to Senbonguchi and take the Yoshino Ōmine Cable Car up to Yoshinoyama when it is running, or walk uphill; from the upper station, the main street still climbs for a long way. Treat the station-to-Yoshinoyama transfer as part of the journey, not as arrival at the sights.