A creature with a spell-like ability limited by "per day" uses will regain that ability 1 day from the time it used it last. As for spells they work the same as the class of which they are casting from; I.E. A cleric will pray to his god at a specific time each day and a sorcerer needs 8 hours rest and 15 minutes in meditation to get them back.

For your more complicated question about 3/day abilities and it only used 1 of its charges then that charge would refresh after 1 day or 24 hours from when it was used however if it used say 1 charge in the morning and 1 charge in the afternoon and 1 charge in the evening they would all return after 1 day from the last time it was used and not the first time.