How do you write a real-time webbased collaboration tool such as google docs?

Google Docs works via operational transformation.

The basic idea of operational transformation is to transform (or adjust) the parameters of an editing operation according to the effects of previously executed concurrent operations so that the transformed operation can achieve the correct effect and maintain document consistency.

Google produced a video about operational transformation for Google Wave; this technology was ported to Google Docs.

As for technology, check out the following links:

• Understanding and Applying Operational Transformation
• Google Wave Operational Transformation
• Real-time Collaborative Editing with Web Sockets, Node.js & Redis
• Operational Transformation library?
• OTpad: Operational Transformations Testing (Etherpad in nodejs)