One thing I look for is the voltage in the circuit, specifically around the IC's. If the voltage is about 5vdc then you can make a pretty good guess that the circuit is digital. Of course, this is not absolute because some analog circuits work off of 5 vdc. But, since a lot of digital circuits work off of 5vdc, its a good starting point.
Another approach is to simply research the IC's used in the circuit. You can look up the IC datasheet and the datasheet will almost always tell you if the IC is digital or not. If the datasheet does not tell you, then look at the Vcc voltage input of the IC. If the VCC is around 5 volts, then again, you can make a pretty good guess that the circuit is digital.
Of course, as Exo explained, most (all?) digitally oriented circuits are a combination of digital and analog. So, some points may work digitally, and others by analog.
In conclusion: Your best bet is to look at the IC's and see if the IC's are digital by looking at the datasheet.