Storage is thread-local by default in D, so nothing is shared between threads unless it is specifically marked as shared. If you mark a variable as shared, you can then use the traditional mutexes and conditions as well as synchronized objects and the like to deal with concurrency. However, the preferred means of communicating between threads is to use the message passing facilities in std.concurrency and let all data stay thread-local, only using shared when you must. All objects passed between threads using std.concurrency must either be passed by value or be immutable, so no sharing occurs there and it is completely thread-safe. However, it can currently be a bit of a pain to get an immutable reference type which isn't an array (idup generally makes it easy for arrays), so it can be a bit annoying to pass anything other than value types or arrays (though hopefully that situation improves soon as compiler and standard library bugs relating to const and immutable get fixed and more code is made const-correct).
Now, while message passing in D will definitely result in cleaner, safer code than what you'd get in languages like C++ or Java, it is built on top of normal, C threads (e.g. Linux uses pthreads), so it does not have the kind of light-weight threads that Erlang does, and so dealing with multiple threads is not going to be as efficient as Erlang.
Of course, I don't see any reason why a more efficient thread system could not be written using D, at which point you might be able to get thread efficiency similar to that of Erlang, and it could presumably use an API similar to that of std.concurrency, but all of D's standard threading stuff is built on top of normal, C threads, so you'd have to do all of that yourself, and depending on how you implemented it and depending on how exactly the thread-local/shared stuff is dealt with by the compiler and druntime, it could be difficult to get the type system to enforce that everything be thread-local with your "green" threads. I'm afraid that I don't know enough about exactly how shared is implemented or how "green" threads work to know for sure.
Regardless, D's message passing system will certainly result in dealing with threads being more pleasant than C++ or even Java, but it's not designed to be streamlined in the same way that Erlang is. D is a general purpose systems language, not a language specifically designed to use threads for everything and thus to use them absolutely as efficiently as possible. A large portion of D's standard facilities are built on top of C, so a lot of its efficiency characteristics will be similar to those of C.