How do you file tax return for a nanny without T4 slip? Is nanny considered self-employed?

A nanny employed in a household is considered an employee.  The employer must do source deductions and do a T4.  If the "nanny" is providing child care services for multiple people rather than one household, they likely would be considered self-employed.

If an employee, they should ask the employer to correct the situation and issue a T4.  The employer will be penalized for late filing and late payment of their share of CPP and EI.  If there is no T4 issued, you could try reporting it as "other employment income", I guess, and wait for the CRA to go after the employer.