In most cases it is impractical for startups to legally have unpaid interns. Under the Fair Labor Standards Act, as interpreted by courts, unpaid interns are only permitted when the employer "derives no immediate advantage from the activities of the intern... and on occasion its operations may actually be impeded" (in addition to other requirements).
By contrast, a paid intern is a type of employee. To hire a paid intern, a startup should use an offer letter and CIIA agreement, just as they would with any other employee.