I've got a circuit full of resistors, capacitors, inductors and logic ICs. Using a multimeter, how would I measure the total current and resistance of the WHOLE circuit?
Run the supply source via an Amperemeter (usually contained in DMMs, Digital MultiMeters) into the circuit.
There are normally two current measurement ranges, 0-200mA and via an extra terminal 0-10 (0-20A).
Using the 0-200mA range make a rough guess of the current flow of your entire circuit. That range is fuse protected and the fuse will blow if 200mA total current are exceeded. Your DMM might be damaged if the fuse doesn't blow fast enough.
Once you have determined the total current flow calculate the resistance of the circuit using Ohm's law.
I've got a circuit full of resistors, capacitors, inductors and logic ICs. Using a multimeter, how would I measure the total current and resistance of the WHOLE circuit?
Note that the current waveform is likely to be very complex, with a high peak to average ratio. There are many kinds of DMMs out there, some of which measure "average" current, and some of which measure "true RMS" current, which is likely to be different than "average" current. Correct interpretation of your reading requires some understanding of what these terms mean, and knowing what your meter reports...