http://www.suite101.com/article.cfm/perennials/14339
In early spring, the fruits will form on the branches before they flower. By May, the tree has fully leafed out. Be careful; fussng with its branches can cause the young fruit buds to drop. The fruits may start dropping by June. This is normal but can cause quite a mess; wasps may also be attracted.
By July the fruits are ripening. The holes at the end of the fruit will open slightly. Figs may also change colour depending on variety.
Some varities have a trickle of sap that attracts pollinators such as ants and wasps; however, garden figs are self-pollinating.
The second crop grows on wood produced this year. It will ripen unaided if your temperatures stay above 15 degrees C for a few months.
http://www.rhs.org.uk/Advice/profiles0303/container_figs.asp
A single crop of fruits can be expected in summer from embryo figs formed the previous summer if protected from frost over winter. Figs are ready for picking when they turn soft, hang down and splits appear near the stalk end of the fruit.
(This info relates to growing in the UK, hence only one crop is expected, however due to recent milder winters it hasn't been unusual to get 2 crops as mentioned in the top article.)
http://www.guardian.co.uk/lifeandstyle/gardening-blog/2008/nov/05/fig-crops-climate-change