You should be able to do this (the .d is because you're in .Net):
alert(data.d.nested.nestedString);
You're accessing the object just as you would in C#, just doing through the properties. The object d is the DummyType you're passing back, so just access the properties on it, the same as they're named in the C# type on the server, that's how they're serialized to the client.
If for some reason I've glossed over something and this doesn't work, remove the .d, but that shouldn't be the case.