How does one determine the power consumption of a device/load in a circuit?
Getting an estimate is fairly direct, although tedious.
You add up the power consumption of every device in the circuit.  Usually with a giant spreadsheet.
You need to take care, particularly with modern digital logic, because the actual power consumption depends on a lot of factors.  But basically you look up the data sheet values, then you add in any power consumed by loads you put on the chip.
I.e., this 74AHC00 chip specifies \$20\mu\mathrm A\$ of draw on the power supply -- but that's just for the chip.  If you were using it to drive LEDs with \$10\mathrm{mA}\$ of current, you'd need to add in \$10\mathrm{mA}\$ for each LED.
So the chip, and each LED would be one line on your power consumption spreadsheet.  Just multiply that by the number of parts on the board, and you have -- tedium.
It's a good idea to overestimate the power consumption on the first cut of a board -- you're never going to get away with just one rev of a board, things are always worse than they seem, and if you're way off on power consumption, it's easier to put in a smaller supply than a bigger one.