Bradycardia:

Slow heart rate. The heart rate is normally slow at rest. 
an arrhythmia that causes abnormally slow heart rhythm, the heart beat is less than 60 bpm. 
Slowness of heartbeat, evidenced by slowing of the pulse rate to fewer than 60 beats per minute. 

Tachycardia:

very rapid heartbeat. 
rapid heart rate, usually defined by a pulse rate of over 100 beats per minute (bpm). 
Abnormally rapid heart beat. 

Palpitations:

irregular, rapid beating of the heart. 
Irregular heartbeats felt as a skip or momentary cessation of the heart. 
The sensation of feeling the heart beat in the neck or the chest. It is often associated with abnormal heart rates and may be perceived as frightening or unpleasant.

An electrocardiogram (ECG) measures changes in electrical potential across the heart, and can detect the contraction pulses that pass over the surface of the heart. There are three slow, negative changes, known as P, R, and T. Positive deflections are the Q and S waves. The P wave represents the contraction impulse of the atria, the T wave the ventricular contraction. ECGs are useful in diagnosing heart abnormalities.

Normal cardiac pattern (top) and some abnormal patterns (bottom). Images from Purves et al., Life: The Science of Biology, 4th Edition