A NuGet client can consume the MyGet package source in the same way it can consume the official NuGet package source.
I am not aware of any documentation for accessing a NuGet package source. However using the NuGet or MyGet package source is fairly straightforward if you use the .NET client library NuGet.Core, which is available as a NuGet package. The main thing that you need is the IPackageRepository interface which has various methods you can use to query the NuGet package source.
An example is shown below that connects to the official NuGet package source and checks if a package exists.
string url = "https://www.nuget.org/api/v2/";
IPackageRepository repo = PackageRepositoryFactory.Default.CreateRepository(url);
bool result = repo.Exists("NuGet.Core", new SemanticVersion("2.8.2"));