You can reach Izu in various ways using the train. The railway systems in this country (which is mostly made for the last Olympic in 1964!) is very intricate and sophisticated. The further the destination, chances are that you have more options to get to where you want.
So anyways, here are the few main ways to come to Izu.
From Haneda airport :
1)Go to Shinagawa station and then change to the Tokaido Line or Shinkansen(bullet train) for ATAMI.
2)Go to ATAMI (either on the Shinkansen or JR Tokaido Line) and then, change to the Ito/Izukyu Line and get off at Izu-ōkawa (伊豆大川駅) !
Please get ready to ask the train staff some questions as the directions are quite complicated.
From Narita airport :
1) Go into inner Tokyo to either Ueno, Tokyo or Shinagawa station (this depends on what kind of transport you’re taking).
2) From Shinagawa or Tokyo, take the JR line, and Go to ATAMI (either on the Shinkansen or JR Tokaido Line) and then, change to the Ito/Izukyu Line and get off at Izu-ōkawa (伊豆大川駅) !
The Golden Route:
1)Somehow find a way to get to Shinjuku Station. (Direct Buses from the airport or by changing lines on the train.)
2)From Shinjuku, take the Odakyu Line to the final destination Odawara.
3)At Odawara, change to JR Line and go to Atami. At Atami, change lines within JR line to get onto the JR Ito Line/Izukyu-Line and head to Izu-Okawa.
*This route is recommended by Rob (janitor) for both price reasons, and aesthetic reasons (also it can be less crowded, as it rarely pops up on google search). Image of how the Odakyu takes you to Izu in the following link http://www.odakyu.jp/english/traffic/railway/.