How to fix a clothes washer faucet that is leaking

Sounds like the packing inside of the faucet needs to be replaced, assuming this is similar to an outdoor hose faucet. After you shutoff the water (probably for the whole house if you don't have a separate shutoff for that line) you can open the valve up by unscrewing the nut that the valve stem goes through. You can find new packing material at most home improvement stores that looks like a black string like material, typically right next to all the washers. I'd also suggest replacing the washer at the same time. And clean all the threads and apply fresh plumbers dope before screwing things back together.

If the installing plumber was nice, you can also unscrew the entire faucet from the pipe. Then clean up the threads, put on some fresh pipe dope, and screw on a new faucet. It will cost a few bucks more, but the process is much easier and the result is also nicer. Unfortunately for me, my plumber decided to solder the threads making this task nearly impossible without opening up the wall to cut the pipes.

If you're not comfortable with soldering pipes should things go wrong, and you have to shutoff the water to the entire house, then consider having an appointment with a plumber already scheduled, that you can cancel without incurring any fees, before starting.

As the comments have pointed out, that is a compression fitting and not a threaded fitting. Removing it should be relatively easy. Loosen the nut by holding the valve with one wrench and turning the nut with another. Once it is loose enough, the valve should just pull off the pipe.

You will have to examine the exposed portion of pipe once you remove the valve to determine if you can re-use the pipe and valve as-is or if you need to cut it inside and install a new stub that you can then install a new valve on. I doubt you will be able to re-use it (its damaged already, hence the leak), so in all likelihood, you will have to replace it. If you do replace it, get a ball valve (1/4 turn) as they are more reliable and easier to operate.

Hopefuly you have an inside shutoff valve for this. If you don't, you will want to ensure you have everything you need before starting this project as the water to your house will be off. If you do have a shutoff then just close it and you can take as much time as you'd like.

Note that you should not use pipe tape or dope on compressing fittings.