Instrument Approach Procedures
Segments and minimums
Approaches have initial, intermediate, final, and missed segments. The minimum safe altitude provides 1,000 ft of obstacle clearance within 25 NM of the fix. Decision altitude governs precision approaches (ILS, LPV); minimum descent altitude governs non-precision. Categories are A (below 91 kt), B (91-120), C (121-140), and D (141-165).
Going below minimums
14 CFR 91.175(c) requires all of the following: the aircraft continuously in a position to land using normal maneuvers and a normal rate of descent, flight visibility at or above the minimum, and one of the listed visual references in sight (approach lights, ALS, VASI, threshold, threshold markings, REIL, touchdown zone markings, runway, runway markings). With the approach lights only, descent may continue to 100 ft above touchdown zone elevation. Red terminating bars or red side row bars tell you the runway environment lies ahead.
Missed approaches and circling
Begin the missed approach at the MAP: the DA for a precision approach, or the fix, time, or DME for a non-precision approach. Circling requires staying inside the circling area for your category at the circling MDA.
Traps
The required visibility is flight visibility, not reported ground visibility. You may never descend below the MDA on a circling approach outside the circling area, and "cleared for the approach" is not permission to go below minimums.
Worked example: on an ILS with a 200 ft DH, you see only the approach lights at DA. You may continue to 100 ft above TDZE and no lower until a runway reference appears.