Go to the local Mages Guild in whatever city you are in. They will usually have an alchemist who sells potions. Skingrad does not have a guild alchemist. If you are there go down the street to All Things Alchemical and say hi to Falanu. Or if you are in the Imperial City, try The Gilded Carafe, or The Main Ingredient, both in the Market District.
Eating a mandrake root will do the same thing, as its first effect is cure disease. In fact you can save yourself a lot of money, and just buy that from the alchemists above instead of the potion.
You can also simply pray at the main altar in any of the chapels. So long as you do not have more infamy points than fame points, or an active bounty, that will also cure any diseases you have.