As stated in the Diagnostic and Statistical Manual of Mental Disorders (DSM-IV), a panic attack occurs when the following criteria have been met:

A discrete period of intense fear or discomfort, in which four (or more) of the following symptoms developed abruptly and reached a peak within 10 minutes:

1) palpitations, pounding heart, or accelerated heart rate:  Typically this is what then generates intense fear as many people believe they are having a heart attack.  This intense fear then exacerbates other symptoms.

2) sweating:  During a panic attack, the body releases little bursts of adrenaline at inappropriate times.  Some of the symptoms of a panic attack can feel similar to the sensations you experience during exercise, such as sweating. 

3) trembling or shaking

4) sensations of shortness of breath or smothering:  Symptoms 1, 4, 5, 6, 8  all exacerbate a panic attack as most people feel as if they are going to have a heart attack and die. 

5) feeling of choking

6) chest pain or discomfort

7) nausea or abdominal distress

8) feeling dizzy, unsteady, lightheaded, or faint

9) derealization (feelings of unreality) or depersonalization (being detached from oneself)

10) fear of losing control or going crazy

11) fear of dying:  Most people experience a strong sense of impending doom.

12) paresthesias (numbness or tingling sensations)

13) chills or hot flushes:  Sometimes the "hot flush" is actually an indicator that the panic attack is ending.  During an attack the body is thrown into a "flight or fight" mode as it prepares for a crisis.  The blood rushes from the head and other parts of the body to the extremities where it is needed (hands and feet).  Once the brain registers that there is nothing to panic about and the attack begins to wane, the blood begins to flow back into the chest and face.  That is what causes the heat or flushed feeling.   

These symptoms are generally what people experience during a panic attack.  However, I find that panic attacks are personal to each person and I am often surprised to hear people's unique symptoms.  If you experience any of these symptoms, please see a doctor right away to rule out other physical conditions.  Once ruled out, work with a therapist who specializes in cognitive behavioral work or panic and anxiety.