What is the simplest way to access data of an F# discriminated union type in C#?

A really nice way to do this with C# 7.0 is using switch pattern matching, it's allllmost like F# match:

var result = someFSharpClass.SomeFSharpResultReturningMethod()

switch (result)
{
    case var checkResult when checkResult.IsOk:
       HandleOk(checkResult.ResultValue);
       break;
    case var checkResult when checkResult.IsError:
       HandleError(checkResult.ErrorValue);
       break;
}

EDIT: C# 8.0 is around the corner and it is bringing switch expressions, so although I haven't tried it yet I am expecting we will be able to do something like this this:

var returnValue = result switch 
{
    var checkResult when checkResult.IsOk:     => HandleOk(checkResult.ResultValue),
    var checkResult when checkResult.IsError   => HandleError(checkResult.ErrorValue),
    _                                          => throw new UnknownResultException()
};

See https://blogs.msdn.microsoft.com/dotnet/2018/11/12/building-c-8-0/ for more info.

Working with discriminated unions is never going to be as straightforward in a language that does not support pattern matching. However, your Result<'TSuccess, 'TFailure> type is simple enough that there should be some nice way to use it from C# (if the type was something more complicated, like an expression tree, then I would probably suggest to use the Visitor pattern).

Others already mentioned a few options - both how to access the values directly and how to define Match method (as described in Mauricio's blog post). My favourite method for simple DUs is to define TryGetXyz methods that follow the same style of Int32.TryParse - this also guarantees that C# developers will be familiar with the pattern. The F# definition looks like this:

open System.Runtime.InteropServices

type Result<'TSuccess,'TFailure> = 
    | Success of 'TSuccess
    | Failure of 'TFailure

type Result<'TSuccess, 'TFailure> with
  member x.TryGetSuccess([<Out>] success:byref<'TSuccess>) =
    match x with
    | Success value -> success <- value; true
    | _ -> false
  member x.TryGetFailure([<Out>] failure:byref<'TFailure>) =
    match x with
    | Failure value -> failure <- value; true
    | _ -> false

This simply adds extensions TryGetSuccess and TryGetFailure that return true when the value matches the case and return (all) parameters of the discriminated union case via out parameters. The C# use is quite straightforward for anyone who has ever used TryParse:

  int succ;
  string fail;

  if (res.TryGetSuccess(out succ)) {
    Console.WriteLine("Success: {0}", succ);
  }
  else if (res.TryGetFailure(out fail)) {
    Console.WriteLine("Failuere: {0}", fail);
  }

I think the familiarity of this pattern is the most important benefit. When you use F# and expose its type to C# developers, you should expose them in the most direct way (the C# users should not think that the types defined in F# are non-standard in any way).

Also, this gives you reasonable guarantees (when it is used correctly) that you will only access values that are actually available when the DU matches a specific case.