Please someone correct me if I am wrong, but I believe that countertenors or, "singing" countertenor is not actually a type of vocal technique, but rather a classification of vocal range.
Much in the same way that one may be classified as a Soprano or Baritone, Countertenor is another voice classification. This term is also used sometimes interchangeably with "male alto" or as Bernstein puts in his Chichester Psalms that a Countertenor may be substituted by boy soprano.
To my knowledge this is not a type of falsetto singing, which is one of the reasons why true Countertenors are so rare. This type of male voice comes from the long since banned Italian tradition of castrating male choir members at puberty. By doing this, men were able to maintain a boyish purity of tone with the presence and volume of a full adult. The resulting sound is quite mesmerizing. Having heard a recording of one of the last true castrati, I can say it is a mysterious sound. But, that is besides the point.
Countertenors may also sometimes be referred to as Irish tenors, and their general tessitura would be more akin to an Alto's range as opposed to a traditional Tenor's range.
Because it is a voice classification, and not a specific vocal technique that can be reproduced, you cannot learn to be a Countertenor any more than you can learn to be a Soprano. Yes, you may learn to be able to fake parts using a falsetto, but there will be a lack of warmth and presence evident in the a Countertenor's voice.
As you may know, voice classification is contingent upon the natural resonating tendencies of and individual's vocal chords. Some resonate more openly, and thus have deeper voices. With training, you can train the vocal folds to be more responsive, thus increasing your range, however, in my experience / knowledge you cannot change the natural tessitura of your given voice.