The short answer is that private citizens cannot.
The CAN-SPAM Act does not give consumers who have received spam email standing to file a private lawsuit for damages.
Instead, private citizens must rely on the Federal Trade Commission ("FTC") or state attorneys general to sue on their behalf to recover damages, impose civil penalties, or impose injunctions. See CAN-SPAM Act of 2003: Role of the Federal Trade Commission; CAN-SPAM Act of 2003: Enforcement by States.
The long answer is more complicated. While private citizens have no federal cause of action, certain states provide private rights of action for violations of state anti-spam statutes. However, many state statutes that deal with spam are explicitly preempted by the CAN-SPAM Act. See 15 U.S.C. § 7707(b); CAN-SPAM Act of 2003: Preemption.