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Even though the atmosphere may be stable to dry parcel displacements, it is often unstable if air parcels become saturated. Remember from the Sounding Diagrams module that an ascending air parcel cools at the dry adiabatic lapse rate only until it becomes saturated. After that, it cools more slowly, at the moist adiabatic lapse rate, and there's a much greater chance that it will cool so slowly that it will become warmer than its surroundings as it ascends. If so, the atmosphere is potentially convectively unstable.
To assess stability to moist convection using a sounding, you need to select a likely-looking air parcel from a sounding, "lift" the parcel, and draw its temperature as a function of height on the sounding diagram. If there's not much of the sounding in which the parcel would be colder than its environment, and a large portion of the sounding in which the parcel would be warmer than its environment, convection is possible.
The intensity of convection closely corresponds to how much of the parcel's ascent path is unstable, and by how much. The upward acceration of the air parcel is proportional to how warm it is relative to the surrounding air, and a deep layer of instability allows the parcel to continue accelerating upward for a long time. A 600 mb deep layer in which the air parcel averages 5 C warmer than its surroundings would imply the possibility of very strong convection, while a 200 mb deep layer in which the air parcel is 1 C warmer than its surroundings would be worth ignoring.
While it's always worth looking at the soundings themselves, meteorologists use stability indices to estimate the degree of instability. The simplest such index is called the lifted index. This is the temperature of the air at 500 mb (in Celsius) minus the temperature of an air parcel lifted from low levels to 500 mb. If the lifted index is negative, instability is present. Lifted indices lower than -5 imply strong instability.
Another useful stability index is called the Convective Available Potential Energy, or CAPE. CAPE is computed as the total area between the parcel's path on a sounding diagram and the environmental temperature, wherever the parcel would be warmer. This area is proportional to the kinetic energy an ascending parcel would attain from buoyancy forces. CAPEs greater than 3000 J/kg or so are quite juicy.
The reason it pays to look at the soundings themselves, though, is that none of this matters if the air parcel can't ascend up to the level at which it first becomes unstable. If there's a layer of very warm, dry air at low levels, it serves as a "cap" or "lid" to convection, since air ascending from below would much colder than its environment within this layer and would sink back down.
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