Once you've met the prerequisites for installing Nexus Repository Manager 3, you'll need to follow a few steps to get it running on Linux.
sudo cp nexus-3.1.0-04-unix.tar.gz /usr/local
cd /usr/local
sudo tar xvzf nexus-3.1.0-04-unix.tar.gz
sudo ln -s nexus-3.1.0-04 nexus
Once you've done these steps you can run Nexus Repository Manager via the following command
./bin/nexus run
You should see a lot of logs come up, and you should be able to access Nexus Repository Manager via the following URL: http://localhost:8081
Voila!