It is advisable to replace your tyres when the tread depth is below 2mm. The legal limit for the minimum tread depth in Australia is 1.5mm.
All tyres have tread wear indicators moulded into the the grooves, when any part of the tread has been worn down to any of these indicators, it is time to replace that tyre. Make sure to check all indicators, as uneven wear could give you false readings if only using 1 indicator.
Furthermore, damage to tyres are seen as side wall cracks and tread cracks due to natural degradation through tyre age; the signs to change the tyres. It is recommended to always change the 2 front, or 2 back tyres at the same time.