When Spider-Man web slings across town, the general procedure is shoot web, hold it, swing, airtime, repeat. For good grip, the end of the web line he's holding should be well below the center of his hand. The average length of a male's hand (measured from the tip of the middle finger to the wrist) is apparently 0.189 m, so we can reasonably assume that the distance from the web shooter nozzle on Spidey's wrist to the middle of his hand is half of this plus a centimeter or two, or about 0.1145 m.
Furthermore, we can approximate the exit velocity of Spider-Man's webs from the nozzle as about 24 m/s.
This means that as soon as he lets go of the webshooting trigger button (i.e. once he's ready to hold the web he has just slung), he has less than 0.00478 sec (4.78 ms) to lift his fingers from the iconic shooting position and then grasp the web in a rope-clenching position. For comparison, it takes a minimum of 100 ms to blink (according to the Harvard Database of Useful Biological Numbers).
Given that super speed isn't one of Spider-Man's abilities, how does he manage to firmly grasp his quickly moving webs as he's swinging around?