Minor blockages close to a fixture are often within reach of basic methods:

Plunger. Works on sinks, baths and toilets. Cover any overflow opening first to maintain pressure, then plunge firmly several times.
Hot water and washing-up liquid. For a slow kitchen sink, a kettle of hot (not boiling, to protect older pipes and seals) water with detergent can shift light grease.
Removing the trap. Under a sink, the U-bend (trap) unscrews. Place a bucket beneath, remove it, and clear any trapped debris.
Drain rods. For an outside drain, rods can push through a blockage in an accessible pipe run.

A note on chemical drain cleaners: they can clear light organic blockages but are best used sparingly. Strong chemicals can damage older pipe joints and seals, are harmful to handle, and do nothing for solid obstructions, root ingress or collapsed pipes. Repeated use is a sign the underlying problem needs proper diagnosis.

Stop and call an engineer if: water is backing up into the house, more than one fixture is affected, an outside drain or manhole is overflowing, or you have tried the above without success.