A few things to think about:
The rings would be in the plane of axial rotation, that is, right above the equator. So how it would look depends greatly on where you live on the planet. If you live on the equator for instance the rings will always look like a thin line in the sky. As you move away from the equator the rings would expand until you reach far enough north or south when you can't see the rings at all because they are below the horizon.
If the planet has a tilt, like earth, the position of the rings in relation to the sun over the course of the year would change. Each latitude would have a distinct "ring shadow calendar", of which duration (how many days out of the year), intensity (darkness of the shadow), and how that darkness changes during the day as the position on the planet enters and exits the shadow would change.
For instance, if you're in a mid-latitude, and you're in "ring shadow season" you may wake up to a sun rise, and then the sun "goes behind" a ring. A few hours later it comes out again and things get brighter, and then darker again as the sun passes behind another ring. At mid-day the cycle reverses itself.
Show a good photo of what this may look like. Imagine you're on the surface, passing through the shadows during the day.
The rings would look like high, dark clouds, and the light/dark transitions would be pretty dramatic.
If you're in the summer season, you wouldn't experience ring shadow at all during the day.
But what would the rings look like themselves? When you're in the summer side of the rings, they would be brilliant, reflecting the sun. The rings would be bright throughout the night as well, but the planet's shadow would also be visible, looking as if it is moving across the rings throughout the night.
You can get a good idea of this shadow here:
When you're in the winter side of the rings, you're on the shadow side or back side of the ring, and they would be dark, though you would still see them due to light reflecting off of ring dust.
Shows a the backside of the rings. Not nearly are bright, but you can see the bands. You can also imagine being on the surface, passing through the different bands of shadow during the day. At night you'll see dim rings and the planet's shadow going across the sky just as you would during the summer.
But what happens during sunrise and sunset? The rings would retain their brilliance, but wherever the light travels farther through the atmosphere, more blue light scatters out, leaving red light. This would be most noticeable after the sun sets, making the portions of the ring that appear near the horizon look orange - just like the moon looks when it rises. So at night (on summer side at least) you get bright rings that go from orange to white back to orange as they span across the sky.
One thought is that summer, especially at mid latitudes, would be a very bright time of year, given the amount of light reflecting off the rings throughout both day and night.