How did the Buddha subdue fear and terror while standing, sitting, etc.?
Buddha has given a detailed answer to handling fear and trepidation in the Sutta SN 11.3. Below I quote the relevant part:


  “But, bhikkhus, I say this: If you have gone to a forest or to the
  foot of a tree or to an empty hut, and fear or trepidation or terror
  should arise in you, on that occasion you should recollect me thus:
  ‘The Blessed One is an arahant, perfectly enlightened, accomplished in
  true knowledge and conduct, fortunate, knower of the world,
  unsurpassed leader of persons to be tamed, teacher of devas and
  humans, the Enlightened One, the Blessed One.’ For when you recollect
  me, bhikkhus, whatever fear or trepidation or terror you may have will
  be abandoned.
  
  “If you cannot recollect me, then you should recollect the Dhamma
  thus: ‘The Dhamma is well expounded by the Blessed One, directly
  visible, immediate, inviting one to come and see, applicable, to be
  personally experienced by the wise.’ For when you recollect the
  Dhamma, bhikkhus, whatever fear or trepidation or terror you may have
  will be abandoned.
  
  “If you cannot recollect the Dhamma, then you should recollect the
  Saṅgha thus: ‘The Saṅgha of the Blessed One’s disciples is practising
  the good way, practising the straight way, practising the true way,
  practising the proper way; that is, the four pairs of persons, the
  eight types of individuals—this Saṅgha of the Blessed One’s disciples
  is worthy of gifts, worthy of hospitality, worthy of offerings, worthy
  of reverential salutation, the unsurpassed field of merit for the
  world.’ For when you recollect the Saṅgha, bhikkhus, whatever fear or
  trepidation or terror you may have will be abandoned.


To answer the question How did the Buddha manage fear? I would say that he recalled Dhamma. If anyone recalls Dhamma, all the fear will vanish or fade away.