Be careful....depending on the make of watch and type of link, it's not quite as simple as it once was ....there may be pins that you slide out or U-shaped connectors (in which case you usually have arrows to show the direction of removal). Some slimline bracelets have pins that are screwed out (look for the tiny screwdriver slot in the end of several pins)...you will need a TINY screwdriver.
I've done this many, many times as I own LOTS of watches!