You can use Webmatrix but its editing and project management capabilities are limited. I would recommend trying Visual Studio Express for Web instead:
http://www.microsoft.com/visualstudio/eng/products/visual-studio-express-for-web#product-express-web
You can open an existing web project in Webmastrix using File -> Open -> Folder as Site.
1. Choose the Demo directory from DayPilot Pro package: http://www.daypilot.org/try.html
2. You can also open TutorialCS or TutorialVB directory from the tutorials: http://code.daypilot.org/
If you want to create a new project, you need to create Bin directory in the site directory and copy daypilot.dll there.