At a glance:

If you were entitled to FTB Part B on 3rd February, you will get a payment of $900 per family. This is a payment from Centrelink.

If you were entitled to FTB Part A on 3rd February and have a child between 4-18, you will get a payment of $950 per eligable child. This is a payment from Centrelink.

If you are required to lodge an 07/08 tax return, you will be entitled to a payment of $900 if you're income is up to $80,000.

The payments from Centrelink will be made between 11-20 March for those that receive their payments fortnightly.
As far as I know, there is no date set for the payments from the ATO.