I've heard that neutron stars are a method of boosting frame shift drive (FSD) jump distance, but documentation seems very limited on them right now. Does anyone have details about how to locate neutron stars, and utilize them? Are there any prerequisites that must be met, in order to use them? I've also heard that using neutron stars can damage your FSD, so how do you repair your FSD on-the-go?
You can find Neutron stars in the galaxy map. You can change the filter to star type, then untick all the letters (f, o, g, k, b, a, m, t etc). Neutron stars and black holes should be coloured grey.
There are no prerequisites to use them.
Once you find one and jump to it, make sure you zero your throttle during the countdown or jump. Hitting the star exclusion zone will get you killed.
You'll see the twin beams. Turn away from the star, and fly out, then into the very end of one beam. As I mentioned above, hitting the star exclusion zone will get you killed so keep your distance.
Sit in the stream for a bit in supercruise, and you'll get a message saying FSD supercharged. Exit the beam to somewhere safe, then go back to galaxy map to plot / replot your next jump. Don't drop out to normal space while in the stream.
Your FSD won't take much damage if you do this once or twice. You can repair at stations. If you are going to make a habit of it out in the middle of nowhere, equip an Auto Field Maintenance Unit, which can be used to manually (not auto) repair damaged modules via the right panel.
Also see https://www.reddit.com/r/EliteDangerous/comments/5738sk/slingshotting_a_comprehensive_guide_to/ And check out YouTube