Some frequently asked questions: (Source - the College of Arms)
Q. Do coats of arms belong to surnames?
A. No. There is no such thing as a 'coat of arms for a surname'. Many people of the same surname will often be entitled to completely different coats of arms, and many of that surname will be entitled to no coat of arms. Coats of arms belong to individuals. For any person to have a right to a coat of arms they must either have had it granted to them or be descended in the legitimate male line from a person to whom arms were granted or confirmed in the past.
Q. What is a crest?
A. It is a popular misconception that the word 'crest' describes a whole coat of arms or any heraldic device. It does not. A crest is a specific part of a full achievement of arms: the three-dimensional object placed on top of the helm.
Q. I am American, can I have a coat of arms?
A. US Citizens who can show a descent from a subject of the British Crown, including from subjects of the Crown overseas in Canada, Australia, New Zealand and elsewhere during the period of British rule, such as India, South Africa and Ireland, can seek a grant of Honorary Arms from the Kings of Arms here. American institutions can petition for a devisal of arms, which is very similar in all but a technical sense.
The descent of arms in England and Wales is determined by the laws of arms, which normally allow transmission only through the male line. The arms of a man pass equally to all his legitimate children, irrespective of their order of birth.
Arms are only transmitted through a female line when there is a failure of male heirs. A woman with no surviving brothers, or whose deceased brothers have no surviving issue, is an heraldic heiress. She is not necessarily a monetary heiress. Providing that she marries a man who bears arms, the children of their marriage may include the arms of her father as a quartering in their own shields. This is how elaborate shields of many quarterings come about.