A number of investigations may be considered in patients complaining of palpitations. Clearly one of the most important is to attempt to get a high quality electrocardiogram (ECG) recording of the patient's heart rhythm during their typical symptoms. If at all possible a full 12 lead ECG is best but often the symptoms are intermittent and smaller devices that can give good quality recordings of the heart rhythm and rate have to suffice.
The links below will take you to descriptions of the various devices that can used and describe which ones are likely to be the most succesful in any given circumstance for different patients.
There may also be other tests that may be appropriate to the investigation of any possible underlying heart disease that might be the cause of the cardiac rhythm disturbance since, whilst many palpitations are an entirely benign (if somewhat irritating phenomenon), others may signal the presence of other pathologies (illnesses) such as coronary heart disease, valvular heart disease or cardiomyopathies. An exercise test and an echocardiogram can be particularly useful in looking for these problems. Whether any further tests or investigations are required is best judged by an experienced doctor who has taken a full medical history from you and examined you.
Your doctor may also consider it worthwhile doing a few blood tests to exclude other precipitants of palipitations such as anaemia, thyroid disease or disturbances in levels of certain salts in the blood (such as potassium, calcium and magnesium).