As I mentioned in an earlier post, I have never had to water my mature fig tree.  Well after experious fruit drop, I now need to.  Question is how long should I water it?  I'll just run the hose to it and let it run for how long?

Ireiley, is your tree in the ground?  If so the hose is not likely to do a good job.  It will tend to channel down and not water all the roots.  Ideally, you would use a good system like the micro sprinklers in this post:  http://figs4funforum.websitetoolbox.com/post?id=4741434
If you don't want to do that, then a soaker hose or lawn sprinkler will do better than just the hose.  As to how long, every soil is different.  The key is to do it long enough to wet the soil down at least 6" deep.   Time it and then dig a little to find out how long for next time.

I would also suggest heavy mulching around your tree.  That will help slow down moisture loss and a fine, heavy mulch can help keep the water from running off as you water.

Yep, tree is in the ground.  I'll use a soaker hose.  This must really be a miserable summer as I have never had fruit drop as a result of drought. 

You will need to figure out how much water you normally get from rain during this period of time, and which is missing this season, and add that much water. Or figure out how much more heat you have had than usual, and add water accordingly.

If lack of water is the issue, identify why you have less water than usual, and add accordingly. It is a diagnostic issue, not a recipe or formula issue. Did you input less water, this season or are you taking more water out.

It could be lack of rain during the growing season, or lack of winter rain (our issue in San Diego last season).

Mulch, about 4-6" is totally beneficial in reducing water loss, and thus reducing the need to input water.