If you already have some JavaScript experience, we recommend you start with our tutorials. If you want to start with the API directly, take a look at how to create a simple app. You can also get started by browsing the ArcGIS API for JavaScript samples or the API Reference.
I just completed a boilerplate example using ASP.NET Web API, Dojo and ArcGIS API for JavaScript. The client side of the boilerplate is coded using the AMD style. You can get the synopsis of this boilerplate at https://github.com/yinshi/WebApi-Dojo-ArcgisApi-Boilerplate/wiki