Effects which happen at the beginning of the turn are similar to End of Turn effects, except that they always happen directly after the "End of Turn" effects for the previous turn. (See End of Turn for more information.)
In addition, if a champion's HP is 0 or below, after all end of turn effects take place, then no beginning of turn effects will occur for that champion. For example, if a champion takes damage from Hive at the end of turn and hits 0 HP, it will be destroyed. If it had beginning of turn healing (such as Regeneration or Intensify), it would be destroyed before that could take effect.