Generally the arm is measured when "cold" or prior to exercise. The arm is held out to the side and bent to about a 90% angle at the elbow. Both the bicep AND tricep muscles are flexed, and the tape is passed around the biggest part of the upper arm.
Some people advocate using a strip of newspaper and then comparing the overlap mark with a ruler or steel tape measure, under the theory that a relatively thick cloth tape measure distorts the measurements.
For upper legs, the measurement should be taken while standing with the legs straight but flexed, and the tape passed around the leg horizontally at the "gluteal fold" - or the crease under your butt.
Calves are measured with the feet flat on the floor, calves flexed, the tape passed horizontally across the largest diameter in the lower leg - which is typically about 1/4-1/3 down from the knee.
All of these should be done by a buddy - it's nearly impossble to do it well on one's own.