The band has two lengths, not one
People say a band is “too long”, as if it were a single measurement. It is two: how many links sit on the twelve o'clock side of the case and how many sit on the six o'clock side. The clasp has to land on the middle of the underside of your wrist, directly opposite the dial, and that only happens when the two sides carry the same length. Take three links out of one side and the total is right, the fit feels tight, and the dial still rotates round to the outside edge of your wrist — because the clasp is now sitting a centimetre off centre and the whole band has to shift to compensate.
So the check is not “is it loose”. Wear it, with your arm hanging naturally, and look at whether the clasp sits directly under the dial. If it does, any remaining problem is total length, and you take a link from each side. If it does not, the problem is symmetry, and you move a link from the long side to the short one rather than removing any. That one distinction saves the most common mistake on this page, which is cutting two links off one side and then discovering the clasp is now permanently off-centre.
Three kinds of pin, three different directions
Before you punch anything, look at the pin with a magnifier. The screw type has a slot in the end and simply unscrews — punching it damages the thread and often the link. The split or cotter pin has a tiny U-shaped split at one end, and is driven out from the plain end. The friction pin is smooth with a slight taper, and is driven out from the thinner end toward the thicker one. Three types, three directions, and getting it wrong jams the pin or splits the link — and a split link is not repairable, only replaceable.
Two more things while the link is open. Many links carry a small bushing that the pin passes through; it drops out silently and the link is loose and rattly ever after. Work over a light-coloured cloth. And when you press the pin back in, support the link from behind — pressing against thin air bends the link ears, which is the second way to ruin a link that was fine.
Or just change the band — but measure the right thing
A replacement band needs the lug width: the gap between the two lugs of the case, measured with a rule, typically 18, 20 or 22 mm. Not the width of the band you are taking off — that is the same number only if the old band was the right size, which is exactly what you are trying to fix. Then check the fitting type before buying: many modern bands have a quick-release lever on the inside, and those come off with a fingernail and no tool at all. Traditional ones use a spring bar, which needs a fork tool. Some cases use screws or a proprietary fitting, and those are not a DIY swap.
Fitting a spring bar: put one end into one lug hole, compress the other end with the fork, and let it drop into the opposite hole. Fit the band face outward — the stitched or convex side away from your wrist. Do not lever at it with a knife tip: the scratch on the outside of the lug is permanent and it is on the most visible part of the watch. And treat the spring bar as a consumable: a bent or weak one lets go on its own, and what it lets go of is the watch.