While i think Lubos answer leaves nothing conceptualy to add, it is on too high level, if you have problem to understand nonconservative fields. Your question is actually freshman topic so i think at first you should understand this in freshman fashion and then move to Lubos answer.
Therefore you might use a very nice resource from OCW MIT by Walter Lewin
It basically tells you to always use Faraday's law. In this framework, as you said, when we have not-changing magnetic field, we get that electric potential drop on any loop is 0 (which textbooks call Kirchhoff II law).
When we have changing magnetic field, than going in the direction of the current (so that you won't have to think about sign in inductance part), you write that the right-hand-side of Faraday's law (that is negative derivative of magnetic flux with respect to time) is simply =$-L\,dI/dt$
Than you do left-hand-side, remembering that ideal conductor has no resistance - therefore there is no electric field in it.
If you still don't get it, here is another resource, or the full lecture