When is deicing required?
There are a few stages where ice prevention or mitigation is relevant. The FAA publishes a nice handbook on it here if you want more info. Very broadly speaking De-Icing activated when airframe ice is noticed. Anti-Ice is activated when a Pilot believes they may enter icing conditions. Ground based De-Ice is applied when icing conditions prevail in the area. 

Before Takeoff

Most, if not all commercial airports offer de-ice facilities if geographically relevant. After the crash of Air Florida 90 the FAA took a bit of a harder stance on De-Ice and now stresses the need for mobile De-Ice units to allow planes to be De-Iced without leaving the taxi queue as well as permanent stations as they have always had. A lot of their suggestions are covered in this AC as well as this one. In this case both airline procedure and FAA regulations will dictate the need for De-Ice. Strictly speaking according to FAR 121.629 a dispatcher can hold an aircraft if they feel it is not correctly De-Iced. However by the same law a pilot can hold their own departure for the same reason. 

En Route

Once in the air there are a few ways things happen, but generally its ultimately up to the pilot to activate the De-Ice system. On one hand the aircraft POH will more than likely have guidance on when to do this, however, airlines may implement further (and more strict) procedures. Some aircraft are equipped with systems that automatically activate in the presence of ice build up.

Once in route there are effectually two kinds of systems,


Anti Ice: prevents the build up of ice in the first place, heated leading edges etc. These are activated before entering icing conditions. 
De-Ice systems: like boots these systems remove ice once its built up. In this case you need to actually enter the conditions and allow the ice to build up first. 


Ice can form in a variety of conditions and can be dangerous or potentially fatal in some aircraft. The temperature depends on the cloud type but generally speaking low temperature and higher moisture content will create worse issues.
 
(source)

Pilots will be alerted to possible icing conditions via an AIRMET ZULU. These are often quite broad area AIRMET's. If a pilot believes they are potentially flying into icing conditions they should keep an eye on the airframe for structural icing build up. Many airplanes have icing lights to help at night with this. A pilot can activate the De-Ice system at any point if they feel it is needed.