I'm a little new to Git, but I've cloned and used a few other repositories before. I've read the documentation on how to clone Boost's git repository, and I know it's more complicated than a normal repository.
Step 1, clone the repository:
git clone "https://github.com/boostorg/build.git" Boost
git submodule update --init
There is a super-project that you need to clone and work from that has (almost) all the current Boost sub-repos linked into it (Boost super-project). You can find further information on how to work in that clone at the wiki. The commands you invoke should look something like this (for non-Windows systems):
git clone --recursive "https://github.com/boostorg/boost.git" modular-boost cd modular-boost ./bootstrap.sh ./b2 headers
But if you just want to get the bleeding edge and deal with git, you can also download snapshot archives from SourceForge for the master and develop branches.