the multimeter in 'amps' mode acts like a jumper wire, so you just connect the meter terminals to the green and white wires (or your blue wires, whatever), polarity doesn't matter if its a digital meter, and when connected, it will turn the furnace on, and read the thermostat current.
note most meters, for DC Amps, you have to move the plus terminal from the normal position to an Amps only position AND switch the meter to DC A(mps). make sure you switch it back to a volts setting or off, and move that meter cable back to its normal position when you are done.