A supply center (or any territory) switches to the control of a Great Power if a unit is in control of it by the end of the Fall Order Phase. A Great Power may then build Armies and/or Fleets to get their number of units equal to supply centers. A Great Power may never have more units than supply centers. When building units a Great Power may only build those units on one of the original supply centers their country owns (example, Austria must build any new units it gets in Vienna, Budapest, or Trieste), though that province must be empty at the time, as there may only ever be one unit in any province at one time.
That about covers it.