Do not get too excited and take action immediately, below are some things you need to check before fixing your clogged sink:
Not all sinks are created equal, make sure that you know the design of your sink before dismantling any of its parts.
Some will immediately run through video tutorials and follow what they watched, unfortunately, if you are copying steps from a different bathroom sink type, you might end up with more issues requiring you to call a plumber.
Most stoppers are made of metal rod and are operated by pushing and pulling it. You may also want to consider the overall lifetime of the stopper, as the older it gets, the harder it is to be maintained.
Most of the households have a set of basic tools, comprising of a screwdriver, slip point pliers, adjustable wrench, etc. If you do not have this yet, you can go to a hardware and buy one. Anyway, basic tool kit is very important not only for clogged sink but other problems too.