If you have a fabric tail, you will be able to wash it in your machine (or handwash it). Always check the manufacturer’s instructions before washing your tail, but most tails can be washed on a cold cycle. If machine washing is not recommended, hand-washing in cold water is what you should do.
You should clean the fabric tail after every use (especially if you’ve been in salt water or chlorinated water). Silicone tails also need to be cleaned after every use. These will have special washing instructions which will come with the tail when you buy it.