You posted in the correct forum...the Tag Forum...so it wasn't a big leap to the Tag link bracelet. I have personnally never done an adjustment on this type of bracelet, but I have worked with both pin and collar and small screws. Screws are by far the easiest. You will need some tools and Esslinger is a source I have used quite often.
I did not include a hammer, but any small hammer can be used. As you can see...a set of screw drivers, a watch bracelet holding block, a pin pusher vise to get the pin started, a good pair of non-magnetic tweezers for handling those small screws, small flat jaw plyers for pulling the pin out, and/or my preference a set of pin pushers to drive the pin out.
Make sure you have a clean well lit work surface. Some form of magnification may also be useful.
Take your time and good luck.
On the other hand, if you don't plan on doing this type of adjustments in the future you may be ahead to save your money and find a good jeweler/watch repair guy for this project.