Take a measured amount of wine and slowly heat it to just before the boiling point (say 210 degrees f). Remove the wine and measure the remaining volume.
Alcohol boils at a much lower temerature than water. By heating the wine, the alcohol will be the first thing to go.
You can assume that the missing volume is mostly alcohol. You alcohol percentage is therfore...
amount missing / amount you started with * 100.
Of course, this method is not exactly acurate, but will at least give you a rough idea of the APV.
Good friends, go in, and taste some wine with me; And we, like friends, will straightway go together (Julius Caesar, Act 2, Scene 2)