TL;DR: AlmostAlmost exactly the same as on Earth.
All the ring really gives you is the location of the equator (well, I guess itit could conceivably be some other spot; the point is that it's a fixed point, no pun intended). Using a sextant, they can get their latitude from this. While it will be faster (and possibly more accurate) than latitude readings on earth, the technique will be substantially the same.
Also, unless the ring happens to have some very visible "landmarks", it won't be useful for calculating longitude; they'll still need quadrants, sextants, and some very good clocks.