The conditions required for contrail persistence are ice-supersaturation. This means that the air is cold and humid enough that the water vapor will directly "condense" out of the air in the form of ice (the process is called "deposition"). Ice supersaturation is around 60-70% of the normally reported relative humidity, which applies to water1.
However, and this leads to the reason why you can't tell from the ground, deposition in most conditions only happens on to ice. i.e. it requires some kind of seed, or nuclei, for the ice to form on. And for ice, this requires a specific molecular framework.
Now actual condensation into liquid is less fussy about what types of nuclei are required. So once the relative humidity in the air goes over 100%, the water condenses out as liquid, and you'll get a cloud.
So you can have a cloudless sky that still has regions (usually in layers) that are ice-supersaturated, but not water supersaturated. When a plane flies through those regions, the water in the exhaust bumps up the humidity over 100%, liquid water droplets condense out. If it's below -40°C/-40°F (yes they are the same) then these droplets will freeze and become ice crystal seeds.
So a contrail starts as a bunch of seed crystals. If the air is ice-supersaturated, these crystals will grow (increasing in mass by a factor of 1,000 or more), and hence can persist for hours, and even spread out to cover the sky.
(1) [FAA, Contrail Microphysics, 2010.] http://www.faa.gov/about/office_org/headquarters_offices/apl/research/science_integrated_modeling/accri/media/Contrail%20Microphysics.pdf