Why does warm air condense into a cloud when it hits cold air? Or, the
same question asked a different way, why does a person's warm breath
condense into a tiny cloud when it hits the cold air and why doesn't
this happen on a warm day?

Dear douglascarey-ga,

This is due to the amount of energy available in the environment in
each case. In the warm environment - the warm air - there is enough
thermal energy to keep the water molecules moving quickly, as vapour.

"Warmer air moving into a region has more thermal energy than the air
it is replacing. At the molecular level we say the average kinetic
energy of the molecules is greater in the warmer air and the thermal
energy of the warmer air is transferred to water molecules by
collisions. The faster moving air molecules transfer momentum to the
water molecules and some of those water molecules will gain enough
thermal energy (or momentum or speed - all three are equivalent) to
escape the liquid and become a free moving gas molecule. If the newly
arriving air is colder the opposite occurs."
  - About Humidity...
    http://www.shorstmeyer.com/wxfaqs/humidity/humidity.html

However, when this air moves into a colder environment and cools down,
like the warm breath in your example, the molecules of water in the
air lose this energy, and as they do so, begin to once again cling
together as they do in liquids - condensation occurs, forming water
droplets, which in turn make up a cloud.

"If air is cooled eventually enough energy will be removed for water
vapor to begin to condense. Remember the water vapor was originally
liquid water and to get it to evaporate you had to add energy. As long
as it has sufficient energy it will remain vapor, but as you cool it
at some point condensation will occur. The temperature where
condensation begins is the dew point temperature. In terms of relative
humidity, as the parcel of air is cooled, the relative humidity
increases, when the relative humidity reaches 100%, the air parcel has
cooled to the dew point temperature."
  - About Humidity...
    http://www.shorstmeyer.com/wxfaqs/humidity/humidity.html

The temperature at which this occurs is referred to as the dew-point
temperature; the temperature at which enough thermal energy is
available to keep a particular parcel of air completely saturated with
moisture. Rather than condensation being something that occurs only
when air is cooled to this point, it is actually occuring all the
time, as is evaporation of water into the air; but above this
temperature, evaporation dominates so that no water droplets actually
form. Below this temperature, condensation dominates.

"Actually condensation is always occurring in our air. At the dewpoint
temperature however, is when condensation overtakes evaporation, and
this is a step in the process of forming dew, clouds, rain, fog,
basically water droplets."
  - "What Exactly Is The Dew Point?"
    http://weathersavvy.com/Q-dew_point1.html

Additional Links:

"Bad Clouds", Bad Meteorology
http://www.ems.psu.edu/~fraser/Bad/BadClouds.html

If this answer isn't quite what you're looking for, please feel free
to request a clarification.

Hope this helps,

cerebrate-ga

Search strategy:

condensation temperature -bose-einstein -
://www.google.com/search?sourceid=navclient&ie=UTF-8&oe=UTF-8&q=condensation+temperature+%2Dbose%2Deinstein
dew point temperature definition -
://www.google.com/search?sourceid=navclient&ie=UTF-8&oe=UTF-8&q=dew+point+temperature+definition

Just an excellent answer and the references were a bonus. This
question has been plaguing me for a while and nobody could answer it.
Thanks.