Agglomerative: every point starts as its own cluster, then the two closest clusters merge — repeat until everything's one big cluster. The order of merges is the dendrogram. Cut it at any height to get k clusters.
Cut height—
Resulting clusters—
Points colored by cluster (at current cut)
Dendrogram — drag the orange line to cut
Linkage matters:single can produce stringy "chained" clusters; complete tends to make tight, compact ones; average is a balance. Hierarchical doesn't need k upfront — pick it by where the dendrogram has the biggest vertical jump.