I don't know if this is a ritual, really, but it helps me mark the season...
Somehow I feel compelled to do a thorough decluttering and housecleaning in the early Fall (and again in Spring). It's sort of instinctive. Banish the clutter now, so our home will be unstressful and lovely to be in during the winter.
I go through all the kids' clothes, decide what to keep/get rid of, decide what to store and how to store it. I tidy all the storage areas - shed, garage, etc. I get the yard cleaned up for Winter so it won't be so icky in the Spring.
Fall pretty much hits around Labor Day here. We start eating cold-weather foods like soups and stews, and drinking hot tea. I bring out the slippers and bathrobes and coats.
I put candles around the house and start lighting them in the evening when it is dark (up on the mantel or other high places when there are littles in the house).
September we enjoy the end of summer and beginning of harvest-time; October is about harvest and Halloween; November is about the coming of winter and our Thanksgiving family celebrations; December brings the transition to winter.
I like the idea of using fall-color-themed napkins/tablecloths, etc, but keep in mind that if you have this tradition you have to store these things.
My kids make decorations and I steer them toward seasonal colors. LOL.
We live in a farming area so there is a lot of harvest-type stuff going on here.
Coming back to add that one of my favorite fall rituals is a hike in the leafy woods. Follow it up with a snack of apples and peanut butter, maybe some cider, and it IS fall.