Age of sail navigation tools for a planet with a ring

TL;DR: Almost exactly the same as on Earth.

All the ring really gives you is the location of the equator (well, I guess it 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.

The ring would assist in navigation at least as much as the stars do. Not only do you have a metaphorical "north/south star" (which would be the apex of the ring), but both the altitude angle and the apparent thickness of the rings would tell you your latitude.

The ring would probably be visible both day and night, and even when you can't actually see the ring apex due to cloud cover or the planet's umbra, you could probably estimate the location of the apex just by filling in the gap in the arc.

In the case where you happen to have a visible feature in the ring (like maybe a shepherd moon), you could also use a calendar and clock to determine your longitude. In the rare case where that feature happens to be at the exact altitude of geo-stationary orbit, you wouldn't even need to know the date/time.

Using a sextant to measure the ring altitude angle or geo-stationary moon would give you a much more accurate measurement of your position, so using a sextant for navigation would be invaluable.