What is the recommended process through pregnancy until birthing.

Hi ladies, it's my first time here in the U.S (N.Y) and I'm not familiar with the procedure within the health system leading up to giving birth, can I get some advice please T.I.A.

SIDE NOTE: back in my home country the process was to join the public health centre and the medical staff will give you appointment dates for check ups until your due date to be admitted to the maternity hospital or if you went into labor you go directly to the hospital to birth.