From my demo samples,
// cairo_surface_t *surface;
// cairo_t *cr;
// surface = call_win32_surface_create_with_dib_T(CAIRO_FORMAT_ARGB32, 240, 80);
// cr = call_create_T (surface);
// call_surface_write_to_png_T (surface, "hello.png");
HDC src = call_win32_surface_get_dc_T(surface); // <--------
BitBlt(dest, 0, 0, 240, 80, src, 0,0, SRCCOPY); // <--------
Assuming that you already have a surface you can use something like the above sample.
dest
is the HDC
handle to the window you want to render the cairo surface.
Update: CView::OnDraw()
You should implement the OnDraw() method for your CView (inherited?) class.
You can use the pDC pointer to draw the cairo surface, ie:
pDC->BitBlt(0, 0, 240, 80, src, 0,0, SRCCOPY); // "HDC src" is mentioned above