There are 2 types of cues: those made of foam and those with padding only.
I don’t recommend washing the tails in the machine, as the foam could become deformed. The padding will absorb a lot of water and could shift. I therefore recommend washing the tail by hand, in a bathtub.
It’s better to target the dirty area than to wash the whole tail. In general, the part close to the floor will be the one to be washed.
If your tail is padded and has a maintenance zip, empty it. You can then machine wash it using the pillowcase technique (see hand washing), or by turning it inside out (see body washing).
Soak the area to be washed in cold water with soap. Gently rub and squeeze the fur to remove the water and dirt. Repeat several times.
Drain the water, then fill the sink with clean cold water. Squeeze the fur to squeeze out the soapy water. Repeat several times.
Drain the water, then squeeze the fur to remove as much water as possible. Dry on a line dryer, flat if possible.
Be careful, the padding can retain moisture for a long time. Leave the tail to dry for several days, if possible with a fan if it’s thick.