Get a Sears water purifier or equivalent, probably lots of suitable units up on Amazon. Make a hooch with water/sugar/turbo yeast. Filter it through a coffee filter, then run it through the machine, throw out the first bit of alcohol. Run it through again if you want.
§5101. Notice of manufacture of still; notice of set up of still
(a) Notice requirements
(1) Notice of manufacture of still
The Secretary may, pursuant to regulations, require any person who manufactures any still, boiler, or other vessel to be used for the purpose of distilling, to give written notice, before the still, boiler, or other vessel is removed from the place of manufacture, setting forth by whom it is to be used, its capacity, and the time of removal from the place of manufacture.
(2) Notice of set up of still
The Secretary may, pursuant to regulations, require that no still, boiler, or other vessel be set up without the manufacturer of the still, boiler, or other vessel first giving written notice to the Secretary of that purpose.
(b) Penalties, etc.
(1) For penalty and forfeiture for failure to give notice of manufacture, or for setting up a still without first giving notice, when required by the Secretary, see sections 5615(2) and 5687.
(2) For penalty and forfeiture for failure to register still or distilling apparatus when set up, see section 5601(a)(1) and 5615(1).
keep in mind having all the material necessary to construct a still is also illegal. It is called "constructive intent."
Like Fly said earlier you can apply for a permit through ATF and distill whatever you want if approved. I would assume bourbon's and whiskeys are a bit easier to get approved since they are typically barrel aged.