How does one downcast a std::shared_ptr?

This ought to work:

if (ptr->IsChildOne())
{
    SomeClientExpectingAChildOne(std::static_pointer_cast<ChildOne>(ptr));
}

The shared_ptr equivalent of static_cast is static_pointer_cast, and the shared_ptr equivalent of dynamic_cast is dynamic_pointer_cast.

Starting from C++11, §20.10.2.2.9 ([util.smartptr.shared.cast]) of the C++ standard specifies the equivalents of static_cast, const_cast and dynamic_cast for std::shared_ptr to be as follows:

std::static_pointer_cast:

template <class T, class U>
shared_ptr<T> static_pointer_cast(shared_ptr<U> const & r) noexcept;

static_pointer_cast requires static_cast<T *>(r.get()) to be well formed. If r is empty, an empty shared_ptr<T> is returned, otherwise returns a pointer w sharing ownership with r where w.get() == static_cast<T *>(r.get()) and w.use_count() == r.use_count().

std::const_pointer_cast:

template <class T, class U>
shared_ptr<T> const_pointer_cast(shared_ptr<U> const & r) noexcept;

const_pointer_cast has similar requirements and semantics to static_pointer_cast, except that const_cast is used instead of static_cast.

std::dynamic_pointer_cast:

template <class T, class U>
shared_ptr<T> dynamic_pointer_cast(shared_ptr<U> const & r) noexcept;

dynamic_pointer_cast is a bit different as it requires dynamic_cast<T *>(r.get()) to be well formed and have well defined semantics. If dynamic_cast<T *>(r.get()) is a non-zero value, returns a pointer w sharing ownership with r where w.get() == dynamic_cast<T *>(r.get()) and w.use_count() == r.use_count(), otherwise an empty shared_ptr<T> is returned.

std::reinterpret_pointer_cast:

For C++17, N3920 (adopted into Library Fundamentals TS in February 2014) also proposed a std::reinterpret_pointer_cast similar to the above, which would only require reinterpret_cast<T *>((U *) 0) to be well formed and returns shared_ptr<T>(r, reinterpret_cast<typename shared_ptr<T>::element_type *>(r.get())). Note N3920 also changed the wording for the other shared_ptr casts and extended shared_ptr to support arrays.