The terms of citizenship are interpreted very strictly. A President must be a natural born citizen, meaning that immigrants are not eligible to run for President, no matter how long they have lived in the United States. If a child of American citizens is born abroad, he or she is technically considered a natural born citizen, and can therefore hold Presidential office. In addition, a Presidential candidate must have actually lived in the United States for at least 14 years, presumably so that he or she is aware of general issues which impact the American populace.
Most citizens also expect a President to be of good character. While people like felons, for example, are technically able to run for President, their campaigns are unlikely to be successful. The morals and ethics of Presidents are often carefully scrutinized, especially by their opponents, so it is generally a good idea to keep a clean slate if you think you might run for President some day.
All American Presidents have been religious, and they have had families as well. Although these two traits are by no means required to run for President, they are expected, especially in the Bible Belt states. Experience is also a useful tool for Presidential campaigns. Most citizens prefer to vote for people who have served in public office before, since it implies that the candidate is experienced in dealing with similar positions. Military experience is also expected of many Presidents, especially those who are old enough to have served in a major war.
Another important aspect of running for President is public speaking and charisma. Presidents must beat a lengthy and often grueling campaign trail, criss-crossing the country in an effort to garner votes. As a result, they must be able to speak persuasively and clearly about major issues while they run for President, especially in Presidential debates. Charisma makes a Presidential candidate more accessible to potential voters, which can strengthen a campaign greatly, as it certainly did during the Kennedy campaign in 1960.