What is grammatically correct she do or she does?

She does is correct, third person singular form of the verb. The form 'do' is used for the first and second person singular and plural; and the third person plural. The form 'does' is used for the third person singular. Example:

• I do
• you do
• he/she/it does
• we do
• you do
• they do

Addition: While the above is certainly true of the indicative mood it ignores the subjunctive mood, in which 'she do' is correct. For example 'I would prefer that she do her homework before she goes out with her friends.'