Netduino applications are built using the .NET Microframework (v4.3), also known as (dot)NETMF. NETMF is an open source project that is further customized to run on the Netduino.
.NET Microframework is a subset of the full .NET framework (roughly .NET v2.0, but without generics support). There is a helpful guide to what features are available in .NET Microframework here.
.NETMF was originally built to run on the Microsoft SPOT watch, so much of the hardware APIs can be found in the Microsoft.SPOT namespace (and child namespaces such as Microsoft.SPOT.Hardware, Microsoft.SPOT.IO, etc..).
.NETMF API Documentation
The .NET Microframework API and SDK documentation can be found on the MSDN site.
Netduino NETMF Customizations
Netduino NETMF customizations and SDK source can be found on the Wilderness Labs github repo.