The best time to fertilize is when the plant starts its active growth in your spring time after the dormancy. Figs normally do not need fertilizer but if you wish to fertilize, you may use any balanced fertilizer. However, a good thickness of compost mulch will do more good in the long run. You may need good thick mulch to preserve moisture, and home made or commercially available compost will do both fertilization as well as moisture preservation.

Also, look at this thread with posts by more fig veterans:
http://forums.gardenweb.com/forums/load/fig/msg0514121131717.html?1

Birdlady 21,

I agree with Ottawan that the best fertilizer is compost. I have used well aged stable compost for 20+ years and the figs respond with strong healthy growth. Also I add a touch of lime each year. If you use fertilizer make sure that it is very low in nitrogen. High nitrogen will put on excessive growth which is undesirable.

Jack

Never fertilized my Brown Turkey even once here in Tempe. Stopped watering after 3 years. I still get 2 crops each year.