Since this is a rental apartment, your first obligation is to notify the landlord or property management as soon as possible, even if it's just by email, so there's a record of when the problem started. This is crucial because if you don't report it now, they can later blame you for negligence if things get worse. Even though it might seem like a trivial drip, what a lot of people don't realize is that behind those stains there can be seepage between layers that degrades the structure without you seeing it from inside, and that's the owner's responsibility to fix.
While you wait for them to act, try to pinpoint exactly where the water is coming from: if the stain is right under a pipe, a radiator, or near where two walls meet, the source could be completely different from a roof leak. Burst or leaking pipes are much more dangerous than a clogged gutter because they damage everything way faster. Place a bucket or a tray under the dripping area to catch the water and take photos of exactly where it's falling, because when the technician comes they'll need that information.
What almost nobody mentions is that the landlord has a legal timeframe to make repairs (usually between one and two weeks depending on your region), so don't let them tell you "I'll fix it when the rainy season ends." Insist that it's an urgent repair because it affects the habitability of the apartment. In the meantime, don't try to seal anything yourself or use adhesives, because that can complicate the diagnosis later and it'll cost you money from your deposit.