How do I follow a path other than the Atlas path?
There are three paths available to you: Explore Freely, Journey to the Center, or the Atlas Path. This is made clear when encountering a Space Anomaly, where you will be given the choice to be given a technology (helping you to Explore Freely), have a black hole marked on your map (aiding you in Journeying to the Center), or be directed to the nearest Atlas Station (pointing you down the Atlas Path).
To "follow" the other two paths, either explore whatever stars you like, or head directly for the center, making use of black hole jumps where you can.