Screen sharing requires a driver to capture the screen and simulate a webcam. There are multiple webcam simulation drivers of this type, commercial and free software packages.
With the screen capture driver enabled you just have to select the new “webcam” in flash (right click the flash and select from settings in any flash video chat software).
Only the user that shares his screen needs to have this type of driver installed. Those running tutoring, consultation, support websites can purchase a commercial software package that includes this type of driver (i.e. Camtasia Recorder with the Live Output feature). Most drivers allow defining a zone to capture and even resizing the output. Chat applications usually require a 320×240 webcam stream at 15fps so you should configure output to that if possible.

Scree sharing solutions:
VH Screen Capture Driver – free for personal use
UScreenCapture – look for Add-ons: Screen Capture DirectShow source filter
MReplay Broadcast – screen sharing driver as service, register on their site to use
Webcam Max – webcam effects, screen sharing, recording, play video, draw on video, picture in picture
Fake Webcam – allows screen sharing or playing video
Virtual Audio Cable – simulates sound device

Another popular method for screen sharing (as seen on youtube), but less professional is pointing your webcam to the screen.

Here is an older test with the VH Screen Capture driver:

For best screen sharing use 2 monitors (ie. laptop screen + external monitor): on one you put the application, window or element that you want to share, on the other you put the Flash video chat application which most probably will also display your screen video feed using the screen-share driver.

Screen size and video streaming size are not the same: The screen sharing driver might capture the entire screen ie 1920×1080 or a zone, but the video chat software might request only a lower  ie 320×240 area.
Different drivers have different ways of handling this:
1) stretch down the whole screen to fit 320×240 or
2) provide only the 320×240 area around the mouse (VH) or
3) provide only the 420×240 area around the center of the screen (Live Output and UScreenCapture).