I've been trying unsuccessfully to use the new .NET resource provider functionality to create a simple .NET provider and resource. Is there an example anywhere I could follow?

A small one in the tests at https://github.com/pulumi/pulumi-dotnet/tree/main/integration_tests/testprovider

Say I created a custom provider;

public class WibbleProvider : Pulumi.Experimental.Provider.Provider
{
  public override async Task<CheckResponse> Check(CheckRequest request, CancellationToken ct)
  {
    await Task.CompletedTask;

    Console.WriteLine("The wibble provider is checking something...");

    return new CheckResponse();
  }
}

I'm not sure how to create a resource type using this provider.

You'll want to fill in the GetSchema method and then invoke the code generator on that. GetSchema just returns a JSON string for a Pulumi schema which is documented here: https://www.pulumi.com/docs/guides/pulumi-packages/schema/ You can invoke codegen by either having a file copy of that schema, or building your provider into an .exe (or linux executable) and then running

pulumi package gen-sdk --langauge dotnet --out sdk ./provider_exe_or_schema_json