How is element search by key within a HashMap data structure performed?

The process of searching for an element by key in a HashMap is as follows:

1. The hash code of the key is computed using the hashCode() method.
2. Based on the hash code, the index of the bucket in the array where the element may be stored is determined.
3. In this bucket, elements are traversed (in case of collisions), comparing keys using the equals() method.
4. If the key matches, the corresponding value is returned.

Thus, searching in a HashMap typically occurs in constant time O(1), but in case of many collisions, the time may increase.