Heart problems may manifest as sensation of the heartbeats (called palpitations, as with rhythm problems), chest pain (usually a feeling of tightness or pressure in the chest rather than frank pain), or difficulty breathing (called dyspnea).
Other manifestations may include fainting (called syncope) either spontaneously or after exercise, edema (swelling) of the legs and various other non specific complaints.
The manifestations depend, of course, on the specific disease and the various characteristics of the patient (age, sex etc.)
You may read more here:
www.nlm.nih.gov/medlineplus/heartdiseases.html