Having joined those two entities into a cluster, the method then searches for the minimum distance between two entites, but taking those entities that are already clustered as a single unit. This process is repeated until there are no more entities to cluster. What differs in the different clustering methods is how the 'distance' is calculated between two clusters that have already formed. This is the simplest cluster analysis method. It has the disadvantage that an outlier can cause two groups of entities to be clustered when most of the entities are really quite distant.
Single linkage tends to form a few big clusters early on in the hierarchy.
This has the advantage over single linkage in that within a cluster, all pairs of entities will be within the distance at which the cluster was formed. Complete linkage tends to form many smaller clusters. The dendrograms have more structure to them and are often more informative than single linkage dendrograms. In 'means' linkage as the name suggests, the mean distance between clusters is calculated. This can be a good compromise between the extremes of single and complete linkage, but the distances at which clusters are formed are averages, not real distances.