The officers of a Delaware corporation are appointed (and removed) by the board of directors. Officers are in charge of managing the company day-to-day.
Most startups start off with at least a CEO and president, a CFO and treasurer, and a secretary. In an early-stage startup, the CEO and president are often the same person in order to avoid any confusion as to leadership, and because the roles are so similar. The CFO and treasurer are usually the same person as well.
There is no limit to the number of offices one person can hold, nor is there any requirement for offices to be held by different people. Solo founders typically hold all the offices in their startup, for example.
Under Delaware law, corporations are not required to define any particular officer titles.1 However, most startups will need to register to do business in their home state, which may require the existence of the typical officer positions.
For most early-stage startups, the primary decision is who will be the CEO and President. Other officer titles tend not to have much meaning, since everyone is doing a little bit of everything and roles are constantly changing.
Offices can usually be added through an amendment to the bylaws, or by the board of directors. Typically, an office must be formally created for a corporation before anyone can hold it. For example, if Chief Technology Officer is not an officer position, you can have an employee with Chief Technology Officer as their job title, but they would not be an officer of the corporation.