A Green Card holder can apply for US citizenship after living in the US for five continuous years. In case of marriage to a US citizen this period is three years.
The US has no rules prohibiting dual (or triple) citizenship.
To apply for citizenship Form N-400 Application for Naturalization must be filed.
Under some hardship-conditions the filing fee can be waived.
You will get an appointment for Biometrics.
You must have the Citizenship Interview and pass the Citizenship Test.
Part of the Naturalization Ceremony is the Oath of Allegiance.
Any children under 18 will automatically receive citizenship too when one of the parents naturalizes. Children over 18 must file their own N-400 application.