K-Means

Pick k starting centres, assign every point to its nearest centre, move each centre to the average of its assigned points, repeat until nothing moves. It is fast, it always converges, and it is usually the first clustering anyone tries.

It also assumes clusters are round, similarly sized and separated by distance, so it fails on elongated or nested shapes. Choosing k is a judgement call informed by the elbow method or silhouette scores, not a result the algorithm gives you.