Analog ground is for analog block and has less noise.
Digital ground is for digital block. The noise is very big.
So it's better to seperate and connect it at board level.
1 - Supose that my circuit has analog and digital parts and I have a power supply. How can I separate the analog and the digital ground if they have the same power supplier?
You would usually have two voltage regulators, one for the analogue and one for the digital devices. The two grounds would be connected together at the ground pins of the regulators. You would use a ferrite bead or a choke to make this join, this will filter out noise. The type and value of the device depends on the frequency's involved.
Another way to reduce noise is to put a capacitor en each digital chip about 0.1uF. Or put a choke betwen the voltage regulator and the digital devices.