How a shirt dries

 Still submerged in water, the shirt will not begin to dry. It is maximally saturated with water. Once lifted out, a great deal of liquid will fall from it rapidly: it was not absorbed into the fibers in the first place, and thus has no way for it to hold on. At this point, more water will be shedded manually, through a process of squeezing or wringing out the excess. Some tub or basin, or the equivalent, will catch whatever falls, if this process should occur indoors. 

Now the shirt is hung, perhaps with companion items of clothing or linen, in a place where any stray drips will caught by the appropriate receptacle--or unto the ground in the case of outside drying. Gravity will pull some of the moisture toward the bottom regions of the garment, such that the upper part will dry at a faster rate. Nevertheless, it is evaporation, rather than this downward pull, that has the greatest overall effect. Thicker or denser fabric will dry more slowly. Warmer, dryer air will accelerate the process. In a hot wind, outside, a wet shirt doesn't stand a chance.