After 3 rounds of study with the spell detect magic, the magic aura will be located (and it might be located on the second round if it's the only aura). Then the caster makes a Knowledge (arcana) skill check (DC 15 + spell level) to determine the spell's school then, if that check's successful, with 3 more rounds of concentration, the caster can make a Spellcraft skill check (DC 15 + spell level) to determine the properties of the magical trap (which I assume is a magic item as it's created using the feat Craft Wondrous Item).
While this will locate the trap and learn the trap's details, that specific trap's precise details could still remain unknown. Ask the GM. For example, the caster may learn that a magic trap is proximity-triggered, but the GM may rule that the caster does not learn the exact proximity that will trigger that magic trap. (This may be the line the GM draws between learning a traditional magic item's properties and learning a magical trap's properties.)
However, detect magic is blocked by "1 foot of stone, 1 inch of common metal, a thin sheet of lead, or 3 feet of wood or dirt," and a trap-maker familiar with magic should build traps knowing that, therefore in such a way that the traps avoid such quick-and-easy detection by what the maker knows is a cantrip or orison. (And, obviously, detect magic doesn't detect utterly mundane traps at all.)