MTG: Legion's initiative rulings?
A turn in Magic is divided into five distinct phases:  the Beginning phase, where you untap, to anything that triggers in the upkeep step, and then draw; a Main phase where you have the opportunity to play lands and Sorcery speed spells and abilities, the Combat phase, a second Main phase, and then the End phase where end of turn triggers happen and then clean up occurs. 

Combat begins after all players have passed during the first Main phase while nothing is waiting to be resolved.  That is when Legion's Initiative returns creatures to the battlefield. This transition is before the attacker has declared whether or not any creatures (and which ones) are attacking.

If you use Legion's Initiative's ability before this point you will get the creatures back on the same turn. If you use it afterwards, you'll get them back on the next turn. 

When a player finishes their first main phase, their opponent(s) can always respond before the Combat Phase starts.  But because responding there is uncommon, it's not unusual (particularly in casual or low level play) for players to announce who they're attacking with without first announcing the end of the main phase.  Feel free to remind your opponent to announce the end of the phase if they haven't been, particularly if you have a card out that has a desirable use at that point.