What are centromeres *really*?
There are many questions in your question. I'll try to answer each question pointwise.


  Which flags are used by the enzymes in the process of making the
  centromere to tell them that it is the right spot


There are some centromere associated repeats in the DNA which mark the site for centromere assembly. There is no particular consensus sequence of this repeat. However, this study says that in certain cases stable chromosomes are formed in the absence of centromeric repeats.


  are the sister chromatids physically intertwined around each other for
  the purpose of joining, or are they simply adjacent?


They are joined by proteins called cohesins. Cohesins looks like rings which form around the sister chromatids. During anaphase, the anaphase promoting complex (APC) activates an enzyme called separase, which in turn degrades cohesin. 


  what in the centromeres do the spindle fibres attach to, and how do
  the tips of the growing fibres notice it to head it its general
  direction?


Centromeres serve as a site for the assembly of kinetochore. Kinetochore is a multi-protein complex which forms contact with the spindle fibres (specifically, K-fibres. Refer this previous post). An essential component of kinetochore is the motor protein dynein which makes the kitetochore to crawl along the spindle fibres, towards the pole. The wikipedia article on kinetochore is quite descriptive and you can refer that for details.