For the most part, rings should not be much of an issue. Most of the rings we know of in our own solar system are made of dust and ice, and outside of Saturn, most of these rings are fairly nebulous. A spaceship moving at orbital or even interplanetary velocity will have a reasonably low chance of impacting anything large (and larger objects like shepherd moons will be fairly visible and easily tracked. Their orbits can be calculated with a high degree of precision and launches timed to avoid them.
That being said, there is still a finite chance for a collision with orbiting space debris (which is really what a ring system is), so a spacecraft operating in the region of the rings would need to be protected with Whipple Shields surrounding sensitive areas (light metal shields held away from the craft by a system of posts. The impact of a hypervelocity particle penetrates the shield, but vaporizes or severely degrades the incoming particles. These shields will need to be frequently renewed the more often you enter the zone of the rings.
Avoiding the equatorial plane is another relatively easy fix. With proper orbital adjustments and timing, the ship could launch on a polar orbit and "pass through" any clear spots (gaps, or coming in over or under the ring)to minimize the possibility of impact. The key issue here is that plane change manoeuvres are very energetic, and require a lot of deltaV from the spacecraft, potentially limiting the amount of manoeuvre possible later as much fuel or reaction mass has to be depleted.
For most work in space, highly elliptical "Molniya orbits" seem to be good work arounds for orbital satellites, providing a long period of "dwell time" in high orbit over the target area for surveillance, communications or other needs, while passing through the rings for only short time.
Highly inclined orbits can also be used to make it more difficult for ring debris to hit the spacecraft. At the most extreme, a ship in a highly inclined geostationary orbit will appear to be doing a figure of 8 over a fixed point on the equator.
So a combination of waiting for good opportunities to present themselves, avoiding the ring altogether (or choosing flight path to minimize exposure), followed by providing some sort of defense to the ship. Sailors navigated treacherous shoals for thousands of years, often with nothing more than a piece of rope for sounding depths and keen eyed lookouts searching for approaching danger. A spacefareing people can do much better of course.