Just before the anti-siphon valve there should be a shut off valve. Turn off the water at that valve and then go outside and check out the hose faucet. The piece that looks like a big nut is what you'll need to twist.
You might need a pair of vise grips or channel lock pliers to hold the pipe while you turn that nut thing with a wrench. You don't want to torque it around while you're undoing the stem.
Once you have it out, the washer is on the bottom. If you bring it to the hardware guy, he can get you the right washer. There're flat ones and ones that are sort of cone shaped. There are O-rings that fit on some, too.
Pay attention to what it looks like and how it all fits together and remember for next time. The faucets on sinks/tubs work more or less the same and you can get the washers for them as well, when you need to. Just get the right diameter and style (flat or cone).
Remember to shut the water off to the brach where you are planning to work! If you don't, you'll end up with water coming out the faucet base and have a hell of a clean up chore.
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