This article is from the Ducatis Motorcycles FAQ, by Duke Robillard firstname.lastname@example.org with numerous contributions by others.
Generally, not very long, just enough until you can keep it going without
it. This can be anywhere from a few seconds to one or two minutes,
depending on the clime. You can feel the side of the cooling fins on air-
cooled models for the beginnings of warmth. When you DO get it to sustain
an idle, start riding but don't rev the motor until it's fully warmed up as
the oil isn't really circulating in the mechanical bits yet, about 10 to 15
minutes or so. An engine will warm up more quickly when it's got a light
load, as opposed to sitting idling away.
No engine should ever be run on enrichened mixtures longer than necessary,
as this is a prescription for premature carbon deposits on your exhaust
valves. Note that fuel-injected bikes have a fast-idle setup, which
obviates worrying about the mixture; it turns off the cold start setup when
its good and ready and you only have control of the fast idle.