The Galaxy Map & Warping
To open the galaxy map, first go into space (you can’t be too close to a base or in an atmosphere,) and then use the quick menu (down on the D-pad or the x key,) and select the galaxy symbol.
The galaxy map isn’t anywhere near as baffling as it may seem at first. Press any button/key to bring up a list of controls for it. You can place waypoints to star systems that interest you for whatever reason, and search for discoveries by other players.
There are a number of filters you can switch between. You can choose a destination star system (as long as it’s in range of your current hyperdrive and you have it sufficiently fueled,) or choose one of the other filters such as the path to the center of the galaxy (probably not a bad idea to start with.) To do that, holds toward the “next star system” until it progresses to it, and the camera will shift from your current location to it.
Whatever you choose, once you’re ready, select the star system you want to warp to, and hold. You’ll initiate a warp jump. You’ll come out of warp in the new star system. Get ready! Sometimes you’ll almost immediately be attacked! If this happens, flee to a space station, or fight it out. If you die, scan for your remains/grave, so you can pick your lost items back up.
Once you’re in this new star system, you’ll receive a new HUD target and mission objective. It will guide you to an outpost on a new planet.