What is Typology in the context of Christianity, and how does it help understand doctrinal matters? What is Typology in the context of Christianity, and how does it help understand, or enhance our understanding of doctrinal matters?

Also, is this something that the Church has always believed historically, or is it something that was introduced at a later time?

Note: I know this is several sub-questions, but I believe that all sub-questions would be needed for a complete answer anyway.  I'm looking for an introduction to the subject for anyone unfamiliar with the term and concept.
From Theopedia:


  Typology is a method of biblical interpretation whereby an element
  found in the Old Testament is seen to prefigure one found in the New
  Testament. The initial one is called the type and the fulfillment is
  designated the antitype. Either type or antitype may be a person,
  thing, or event, but often the type is messianic and frequently
  related to the idea of salvation. The use of Biblical typology enjoyed
  greater popularity in previous centuries, although even now it is by
  no means ignored as a hermeneutic.
  
  Typological interpretation is specifically the interpretation of the
  Old Testament based on the fundamental theological unity of the two
  Testaments whereby something in the Old shadows, prefigures,
  adumbrates something in the New. Hence, what is interpreted in the Old
  is not foreign or peculiar or hidden, but arises naturally out of the
  text due to the relationship of the two Testaments.


The use of Typology is useful in several applications.  


An understanding of typology demonstrates the harmony between the Old and New Testament, as in the phrase "The New is in the Old Concealed, the Old is in the New Revealed"

Typology is also helpful helping us to gain a deeper understanding of important principles.  
Typology helps us to understand who Christ was, and bring deeper meaning of Him by understanding the types that prefigured Him.
It is also used in attempts to understand prophetic works.   Again, from the Theopedia article:




  For instance, the promise of Genesis 3:15 is cast in terms of the
  struggle between men and serpents, and yet it contains the Gospel, as
  the Seed of the woman crushes the head of the Serpent once and for all
  on the Cross; it is for this reason that this verse is called the
  Protevangelium.


While Typology is commonly used within Catholic, Orthodox, and many Protestant denominations, it is discounted by many more liberal scholars:


  Lampe argues that, historically speaking, typology was traditionally
  understood as the real meaning of the Old Testament - a meaning read
  into it by the Holy Spirit, even though no one in the OT could have
  understood it. He concludes that not only is this old fashioned and
  out-dated, but typology is no longer to be pursued.
  
  Gerhard von Rad, who writes from a rather Neo-orthodox perspective,
  understands typology as just more or less analogical thinking.


For those that do not discount typology, many see it as a validation of the doctrinal concepts of Inspiration of Scripture, and infallibility.  To proponents, the clearly visible types and antitypes revealed in the Old and New Testament show God's handiwork throughout Scripture.  The perfect unity and harmony in books written many years apart from each other, by many different authors, with very different backgrounds, yet in agreement in so many points, with prophetic events is seen as nothing short of impossible if we were to try to imagine such things arising without divine influence.


  Typology represents a vital part of early Christian hermeneutics built
  upon the belief that God is in control and has unified His Word and
  the events in redemptive history.^[6]^ It is questioned whether
  typology is prospective (the OT type as a divinely ordained
  prediction) or retrospective (the NT antitype as analogously related
  but not prefigured in the type). It is likely that the solution lies
  in the middle. The OT authors and participants did not necessarily
  recognize any typological force in the original, but in the divine
  plan the early event did anticipate the later reality. Thus David's
  coronation (e.g., Psa. 2, 72, 110) did indeed foreshadow Jesus'
  enthronement as the royal Messiah, though it was not a direct
  prediction.


Whether it is valid or not as an approach toe eschatology or hermeneutics appears to be, controversial at best, it can be safely said that it is an approach to understanding Scripture that dates back to the earliest days of the Church.  This is no "new idea" that was snuck into Christianity, or was added to it later. The use of typology is as old as the Church itself.

Paul himself found it useful in illistrating certain concepts.  For example:


  1 Corinthians 15:45  (KJV) And so it is written, The first man Adam was made a living soul; the last Adam was made a quickening
  spirit.


In the above passage, we have a Scriptural use of typology - a standard type that is still preached today - Adam as a type of Christ.