The D language reference compiler is called DMD (Digital Mars D). Also available are LDC (a LLVM-based D compiler). and GDC (a GCC-based D compiler). See the Compilers wiki page for more detailed information, but if you're new to D and aren't sure which to install, install DMD.
The D downloads page provides an overview of the various D implementations, and contains links to pre-built OS-specific DMD packages ready to download and install.
As an alternative to the OS-specific packages, there's also an install script for use with any Posix-like System (Linux, FreeBSD, MacOS) that can install the various implementations (including multiple versions of them) locally without requiring any administration rights. See the install script documentation for details.
The beauty about D is that you don't need a fancy IDE as boilerplate code is very rare. However, using D is nicer when you are in the comfortable zone of your favorite editor. There are D plugins for at least the following editors:
You may also want to try an IDE dedicated to D:
The D wiki contains a more detailed overview of available editors and IDEs.