Like Harbinger said, Passive Perception is what they notice without actively searching. When they actively search, they roll a d20 and add their Perception modifier (Wisdom modifier + 1/2 level + 5 if trained + other modifiers). Actively, they may miss something that they would have noticed accidentally, depending on the circumstances.
For determining DC, it matters what level they're at. At levels 1-3, DC 5 is very easy, DC 10 is moderate, and DC 15 is hard. They each increase slightly by level (you can find the list of average DCs in the updates for the DM's Guide on the Wizards of the Coast official site). On level 1, a +5 in a skill usually means that they are trained, or are naturally good in that skill (with a racial bonus), so they can (in the case of Perception) notice things that are technically "hard" to notice with a Perception check.
Hope that helps!