The power to supply an average home for a year would produce some high level waste (about as much as a sheet of paper). A little more low level waste.How
How much waste does it produce and where are they storing it now? What do countries such as France that are almost totally nuclear do?
Spent rods are stored in water to decay. At some point they can be moved into a canyon and stripped using a chemical process.
We had the Mixed Oxide Fuel project (MOX) but that was scrapped a few years ago. We get tritium from rods as well.
The waste goes into a tank farm. The waste stream is split (chemically) into high level and low level waste. The high level waste is turned into a type of glass and stored in stainless steel vessels. The low level waste is mixed with a grout like substance and stored in tanks.
In Los Alamos containers are stored 2150 feet underground in limestone tunnels. Over time the limestone encapsulates the containers.

. Of course there are exceptions like deploying Marines and Rangers to some god forsaken country and delaying pay so their families have to go on welfare to make ends meet. Isn’t that the American way?