How to identify a VCC pin on PCB use digital multimeter?
Turn the board on, turn the DMM to measure DC voltage up to 20V (or auto range), put your black probe to a ground pad an look for some capacitors - electrolytic, tantalum or even SMD ceramics which look thicker then others. Put your red probe on capacitor's (+) pin/pad and check if this is the desired voltage (3.3V). Then if you are looking for a more convenient to use pad you can turn off the device. Test with the multimeter if the voltage is fallen enough (below 0.5V), switch the DMM to measure diode, put one of the probes on the pad you already know is VCC from previous measurement an search for a pad on which if you put the other probe the DMM will say "0.000" or similar.

About measuring continuity and diodes. Actually these tests are quite similar, even on some models both test are combined. The difference is that continuity test show on the display something close to the ohmic resistance of the connection, while diode test shows mV of PN junction. 

Most commercial DMMs inject curent and measure resulting voltage. That's because it's simpler and much more accurate to inject a predefined constant current and to measure low voltage than measuring very small current, resulting form a constant voltage. The current depending on DMM's model is between 0.1mA and 2mA and is very unlikely to burn anything. There are 3 main reasons you have to make a continuity measure on a turned off equipment


for a HV equipment it can burn your DMM, not the equipment itself; 
for a sensitive LV equipment multimeter's current can change some input's state and lead to undesired response of the system; 
when you place your probes over a certain voltage (say 1V or more) in one direction your DMM will state "connection", on other direction it will say "disconnected" and none of them would be true :)