I have a cloth napkin system.
TBH, there's pretty much always a single napkin sitting on the kitchen table, which I use for weeks and weeks, usually.
If it needs cleaning, I hang it on this gate that leads to the laundry room, and I grab it when I go into the laundry room.
They are washed in my washing machine with my clothes either on cold/cold or warm/cold, depending on my mood, with some biodegradable fragrance-free laundry powder from the local refill store.