Vinegar has many applications in food and cooking, from marinating to pickling. You can also thicken vinegar through a process called reduction to make a glaze, sauce, drizzle or other dish accompaniment. This is usually done with balsamic vinegar. When you reduce the vinegar, it's also possible to flavor it in numerous ways to better complement and enhance the food you're using it on.
Measure out about four times as much of a thin vinegar as you want to end up with once it's reduced and thickened. Measure out about three times as much if you're starting with a thick vinegar.
Pour the vinegar into a small skillet or saucepan. Bring it to a boil over medium-high heat.
Reduce the heat to medium to simmer the vinegar. Add in other flavorings you've chosen. For example, a bit of honey or brown sugar adds sweetness to the vinegar reduction. Fresh rosemary or thyme are classic additions for use on meats and fish.
Check the vinegar periodically to maintain a steady simmer, adjusting the heat a little up or down as necessary. Other than this, no stirring or other action is necessary while the vinegar reduces. Watch it more closely as it approaches the desired thickness so you don't over-reduce it.
Remove the vinegar from the heat source when it's just about as thick as you want it -- it will thicken slightly more before it cools. This can take anywhere from a few minutes to about 30 minutes, depending on the starting thickness, the volume of vinegar and how thick you want it.