Reduction changes cheap balsamic vinegar into a richly-flavored syrup.
Step 1: Acquire ingredients
After tasting a friend's heirloom-quality balsamic vinegar our regular balsamic made us sad, though not sad enough to justify a $100 tiny bottle of vinegar. Reduction is a much cheaper route to a flavor that's at least reminiscent of the good stuff.
True balsamic vinegar tradizionale is made from cooked grape juice slowly aged in a variety of wooden casks for a minimum of 12 years, developing an intense and complex set of flavors and slowly evaporating excess water. The longer the aging the better the resulting vinegar.
The balsamic you and I can afford is actually sweetened wine vinegar combined with caramel color. A good version of the inexpensive stuff is sweetened with reduced grape must (whole juice), and will have 3 ingredients on the label. A bad version will have a longer label list, probably including nasties like high fructose corn syrup. Read the label carefully. We used Trader Joe's balsamic, which is a reasonable balsamic of the three-ingredient variety.
So, you will need:
1 bottle balsamic vinegar
1 heavy-bottomed pot
1 stirring implement
some free time