How do you tell the optimum time to pick the only fig that has ripened on a tree?

1. protect it from critters
2.  wait for full color
3. it should be soft and droopy.  Don't bother checking for softness until it's droopy
4. there may be superficial cracks in the skin.  DON'T PANIC!
5. if it bursts pick it right away
6. protect the plant from excess water to prevent #5  and develop the best flavor
7. Give it as much heat and light as possible.

See Growing Tips / Harvest

Every variety is different, so you will have to experiment a little. Almost without exception you will be tempted to pick it 2-3 days too early.

Jon, I know and that is why I don't want to mess up on the only one this season. It is fairly soft but not droopy yet.

Bob, thanks for your advice.

Basically Mike you will just know it will hang loose and maybe drip some nectar from the eye Maybe this will help you out    http://www.squidoo.com/fresh-figs

Small answer.

Never do this:

As soon as the fig swells; cut it and taste it.

If sweet, it must be ripe.

If latex oozes from the stem, it probably needed 1-3 more days;
try attaching it back on the tree for later ...