What each part of a bridle does
Follow the straps from the poll to the reins to understand how a conventional bridle is assembled.

Start at the top
A conventional English bridle can look like a tangle when it comes off its hook. Hold it by the headpiece and let the straps hang freely. The headpiece passes over the poll, behind the ears. The browband runs across the forehead and connects the sides. Its job in the assembly helps explain why a browband that is too short can affect more than the forehead itself.
The cheekpieces descend towards the bit. Their buckles allow adjustment, although adjustment holes do not make every size suitable for every head. A throatlash passes beneath the throat area. It is a different strap from the noseband and should never be identified simply as whichever buckle happens to be nearest when you pick up the bridle.
Trace one connection at a time
The noseband may have its own narrow head strap or attach to the main headpiece in another way. Designs vary considerably. Before taking a bridle apart for cleaning, photograph both sides and label the separate pieces if necessary. The arrangement on a friend's bridle may not match yours, even when both are described as snaffle bridles.
Reins attach to the bit on a conventional bitted bridle and provide the connection to the rider's hands. Buckles, billets and clips are different attachment systems. Learn how your particular fastener closes fully, including the use of its keepers. A fastener that looks shut from the outside still needs checking; a twisted strap or trapped keeper is easier to spot with the piece held in good light.
Names help when something is wrong
If a buckle sits awkwardly near the eye or a strap approaches the corner of the mouth, describe which piece is involved rather than shortening everything at once. The whole assembly needs assessing together. Mixed component sizes are sometimes appropriate, but compatibility and final fit should be checked by a qualified bridle fitter.
Never tighten a noseband to hide mouth opening or other signs of discomfort. Those signs need investigation, including the horse's mouth, teeth and equipment as appropriate. Once the bridle is correctly fitted, keep a record of its arrangement for cleaning and reassembly. Recheck rather than blindly copying old holes when parts, horse condition or equipment have changed.