I received one of those pints of mass produced, 100% corn whiskey as a gift. Rather than suffer through it, I thought I'd try to improve it!

Step 1: Ingredients/Supplies

1 - corn-based "moonshine"
2 - pieces of oak
3 - a clean, wide-mouthed jar
4 - blowtorch or grill
5 - funnel
6 - water filter/pitcher
7 - cheesecloth

Step 2: Scorch That Oak

Use a hatchet to split some oak scraps into smaller blocks. Make sure these will fit in the jar!
Thoroughly char the blocks. Brings a little smokey flavor to the end product.

Step 3: Add Whiskey and Wait

Place the oak into a clean jar, then carefully pour in the rot-gut whiskey. Tuck it away in a dark corner and wait. As the wood soaks up some of the alcohol you may want to add more.
The color improves quickly. These before-and-after shots were taken 12 hours apart!

Step 4: Filter and Bottle

Wait weeks and weeks. I let this first experiment go for an entire month. At some point it'd be fun to make several batches and see where the point of diminishing returns is hit. That would require actually buying this cheap whiskey on purpose, though...
I had a Brita filter in need of changing, so I used it to filter my whiskey for its last hurrah. (Gives me a reason to scrub the pitcher thoroughly, too.) Small amounts of charcoal from the filter may pass through. For this reason you may want to use a piece of cheesecloth to line the funnel before you fill up a new, clean bottle.

Step 5: Enjoy!

Results!
Color: much improved
Taste: not nearly as cloyingly sweet, and even picked up a bit of the oak and smoke flavor from the wood. Filtering it through a Brita also improved it greatly (relatively to its original taste).
Bonus: whiskey-soaked oak pieces for your grill or smoker!