Fluffy can be bathed in warm water, optionally with oats as a cleaning agent.
She can swim but it is most comfortable for her if there is shallow space for her to paddle in.
When cleaning her, use both hands to hold her with her quills down submerged in the water, and her face and soft front upwards in the air so that she can breath and hold onto your topmost hand, this softens the outer layers of the quills. After holding her this way for 2-5 minutes use a wet toothbrush to clean her quills using a brushing motion along the grain of her quills.
After bathing, dry her off with a towel, and then wrap her up in a different towel.
If you are cutting her nails, this is time to do it, when her nails are softened by the water. Use the little scissors to cut any excess length from her claws, being careful not to cut her feet.
Once Fluffy is wrapped up in a towel, hold her against your body in the towel. Hold her this way for the next 30-60 minutes, so that she can equilibriate with your body temperature. She is usually quite still while drying off, although she will occasionally wriggle into a better sleeping position.
Make sure that Fluffy is dry before returning her to her tank. Any moisture on her body will evaporate, taking some of her body-heat away with it, and leaving her colder.