Borderline personality disorder (BPD) and other personality disorders are typically diagnosed using the official guidebook for the diagnosis of psychiatric disorders, the Diagnostic and Statistical Manual of Mental Disorders (currently in its fourth edition, the DSM-IV-TR).
The DSM-IV-TR uses a "multi-axial" diagnostic system. This means that when a diagnosis is made, attention is paid to five different areas, or axes, that may affect the individual being diagnosed. Axis I is for the diagnosis of clinical disorders; these are the conditions that people most often think of when they think of psychiatric disorders. For example, major depressive disorder or posttraumatic stress disorder would be diagnosed on Axis I.
Axis II is reserved for long-standing conditions of clinical significance. Personality disorders and mental retardation are diagnosed on Axis II. These disorders typically last for years, are present before adulthood, and have significant impact on functioning.
In theory, personality disorders are relegated to Axis II because this is a way to make sure that these disorders do not get "lost in the shuffle." If a person has multiple clinical disorders on Axis I, coding the personality disorders on Axis II can help them to stand out.
Another reason that experts decided to put personality disorders on Axis II relates to the course of these disorders. Whereas Axis I (clinical) disorders tend to be episodic (i.e., they are on-again, off-again), personality disorders are thought of as chronic over years. However, research has suggested that personality disorders are not necessarily as long-standing as previously thought (see this article on BPD prognosis).
American Psychiatric Association. Diagnostic and Statistical Manual of Mental Disorders DSM-IV-TR Fourth Edition. American Psychiatric Association: 2000.
Westen D, Shedler J. Revising and assessing Axis II, part II: Toward an empirically based and clinically useful classification of personality disorders. American Journal of Psychiatry, 156(2):273-285, 1999.