You can install the RC with e.g.:

pip install astropy==3.2rc2

and test it with (make sure you have the dependency pytest-astropy installed):

python -c "import astropy; astropy.test(remote_data=True)"

Or if you don't want to install (and/or want to test the docs files, too), you can do the following, assuming you have pytest 3.5+ installed:

pip download astropy==3.2rc2
tar xzf astropy-3.2rc2.tar.gz
cd astropy-3.2rc2
python setup.py test --remote-data

This will produce a long sequence of dots and letters indicating the test is running. At the end you should see something like

=========== 8949 passed, 115 skipped, 73 xfailed, 1 xpassed, 2 pytest-warnings in 476.85 seconds ===========

If this shows no failures, you can report it in the table below as a "success", otherwise put it as a "failure" (and if need be you can create an issue in the astropy issue tracker).

If you are in a hurry and already have the astropy git source set up, you can also just checkout the v3.2rc2 tag. Don't forget to fetch the latest changes first (git fetch --all). Note, though, that the pip (or downloading the pypi tarball and installing it) is preferred, because that's closer to what users will do.