Are you interested in hand pollinating your figs or breeding different varieties?
These are steps taken from an older book on fruit breeding.
The first attempt to improve figs through pollination began in 1908. Before that time all fig varieties were selected from wild or naturalized trees (maybe mutations of known varieties too?) and propagated by cuttings. Dr. Ira J. Condit did extensive fig breeding in the 1900s, he might have some interesting research papers.
The breeding work starts when you decide on two parents you want to use in a cross. One will be the "male," and supply the pollen. And one will be the "female" and form seeds.
The only crop on a fig tree that produces pollen is the crop that is produced on dormant wood, from buds that over-wintered in the fall, also known as Profici. To harvest pollen from these fruit cut them in half long ways, and place them in a warm, dry place with little air circulation to dry and release pollen. It is recommended that you dry the figs on top of some kind of paper.
After several days they will begin to release pollen which you can shake out by tapping the fig with your finger or a pencil. This pollen can be put into containers with sealed lids, like vials, pill bottles, or mason jars, and stored in the refrigerator (around 8-10 degrees C, 46-50 F) for as long as 120 days.
Also note it is best to dry different varieties of figs in different rooms as their pollen is so light that cross-contamination can be a problem.
The figs that form on the currant season's growth are the ones that you pollinate with your extracted pollen. These fruit are your "female" fruit and do not produce pollen. They only produce pistols, the female part of a flower which receives pollen. To pollinate them take an ice pick, nail, or similar instrument, and make a hole halfway through one side of the fig, followed by another through the eye or in another location on the side of the fig. This second hole allows for air circulation as you blow pollen into the fig. Take a pipette or syringe and puff the pollen into the fig through one of your holes. You are blowing pollen into the inside cavity of the fig which is covered with receptive female pistols. Any way to get pollen into this cavity should work well. There is even a report of a breeder who cuts a fig almost the whole way in half, pollinates it, and it still forms a mature fig.
Carefully mark the crossed fig to keep track of the cross. When I breed other types of fruit I like to cover crosses with a small bag made of floating row cover for vegetable production (brand-name "agribond" or "reemay") which lets light and air circulate, but protects my cross from weather extremes and hungry passersby, animals and people!
After the fig matures it needs to be fermented to remove the gel surrounding the seeds. Cut it into several pieces and drop it into a jar with water to ferment for several days. It will need to be shaken several times. The process is the same as saving seed from tomatoes. It might also work to scoop out only the gel and seeds from the cross and exclude most of the flesh of the fig. That would make cleaning easier. After fermenting, the seed can be washed with clean water and dried or germinated immediately.