The short answer
Wind a vintage mechanical watch slowly and gently. If it is a manually wound watch, turn the crown until you feel a definite increase in resistance, then stop. Never force it.
With an automatic watch that has stopped, a small amount of hand winding can give the movement enough power to get started before normal wear takes over.
From the bench
Winding a watch is doing something very simple: storing energy in its mainspring.
In a manually wound movement, turning the crown winds the mainspring progressively tighter. As it approaches fully wound, the resistance through the crown increases. That change in feel is the watch telling you it has had enough.
There is no benefit in forcing the crown beyond that point.
Most automatic watches work differently. Their rotor winds the watch as it moves on the wrist and the mainspring generally uses a slipping bridle, allowing it to slip when sufficiently wound rather than being wound rigidly to a stop.
That is why an automatic watch doesn't normally reach the same firm stopping point at the crown as a traditional manually wound movement.
Some vintage automatic movements can be hand wound and some cannot, so it is worth understanding the particular movement in your watch.
What we recommend
For a manually wound watch, make winding part of your daily routine. Wind it slowly, preferably at roughly the same time each day, and stop when the crown gives you clear resistance.
For a hand-windable automatic that has completely stopped, around 15 to 20 slow turns of the crown is usually plenty to get it started. Put it on your wrist and allow the automatic winding system to do the rest.
Don't chase an arbitrary number of turns. Feel is more useful than counting.
And if the crown becomes unusually stiff, gritty or behaves differently from normal, don't force it. A vintage watch should never need an argument with its owner.
Mechanical sympathy is usually the best tool you can give a vintage watch.