How can I fix a clothes washer faucet that is leaking?
The stem should be able to be removed after unscrewing the part of the faucet as pointed to here:



Remove the red tap handle first. Then use a pair of wrenches, one on the indicated part and the other on the faucet body to loosen and remove the threaded part. The usage of two wrenches is very important because you do not want to stress the soldered pipe the goes off into the wall. 

I have found the following type of groove lock pliers to be one of the most effective tools for this type of job. The fine range of adjustability and the jaw shape make the grip to the faucet parts easy. Do note that these tools can cause marks to appear on the faucet parts, especially of soft brass or bronze materials or if the threaded part is really tight.