How to do desktop sharing web application

Basically you will want to take screenshots and you can transmit those screenshots and display them on the other side. You can keep the last screenshot and compare the screenshot in blocks to see which blocks of the screenshot you need to send. You would typically do some sort of compression before sending the data.

To have remote control you can track mouse movement and transmit it and set the pointer position on the other end. Also ditto about keystrokes.

As far as compression goes in C#, you can simply use JpegBitmapEncoder to create your screenshots with Jpeg compression with the quality that you want.