The DocuWare Platform provides access to DocuWare. You will find all features provided which are used by the DocuWare WebClient.
The DocuWare Platform .NET API is a set of .NET assemblies which are used to simplify the access to the DocuWare Platform for .NET programmers.
You need a Visual Studio 2012 installation of any edition. Then you can install the needed libraries using the 
NuGet package manager. Just type "DocuWare" in the search box of the package manager or install it in the Package Manager Console running Install-Package DocuWarePlatformApi.
After you installed the package you might want to take a look at the code samples and read The Platform as REST Service.
The .NET API supports both synchronous and asynchronous patterns. You can get familiar with the patterns.