Don't let yourself be talked into getting some "universal" kit that works for everything - those are a disaster. I tried one years ago with an old faucet and ended up spending more money on failed attempts than I would have if I'd just called a plumber. The key is knowing exactly what model you have before you even touch Amazon.
Once you know what you're looking for, though, it's honestly a really easy job. I still end up changing them now and then for friends who have decent faucets - nothing complicated. Turn off the water from the valve under the sink (or from the main one if there isn't a shut-off valve there), take apart whatever needs to come apart, pull out the old seal which is usually hardened rubber, pop in the new one and put it back together. The cost is minimal, like 10-20 euros for the right part if you find it online, less if you go to a plumbing shop where the old-timers know their stuff and will give you solid advice. Time-wise? Twenty minutes tops if you're not in a rush and you're not the type who usually ends up fighting with screws.
The important thing is not to use overly aggressive pliers when you're taking it apart because you'll damage the faucet itself, not just the seal. And if the faucet is really old and the internal seat is pure corrosion, then yeah, it's worth replacing the whole thing. But from what I'm imagining of a faucet that's been leaking slowly for months, it's almost definitely just the seal, and that's really a job anyone with two hands can do.