Apply 3 months before the date you plan on giving your exam. The registration, verification and application processing will take 2 months max. The remaining 1 month is to book your exam date in advance so that you can be sure of getting the date you want.
When you apply, you need to select a 3 month eligibility period. So since you want to give your exam in march, select Mar-May or Feb-Apr so that you fall within the eligibility period in case you need to postpone your exam.
You can extend this 3 month eligibility period by another 3 months.
You can book your date once you get the scheduling permit which is only once your application is processed. You can reschedule multiple times for free as long as its 31 days before the exam date. If you reschedule within a month of the exam date you need to pay a fee which is given on the ECFMG site.
Hope this has cleared everybody's doubts.