my outdoor faucet seems to be leaking. My gf wrapped it up with tape to try to reduce the flow (bless her) I don't know what pipe or piece seems to be connected under the actual spigot. Does anyone have an idea of a fix or replacement method?
If the pipe itself is cracked and leaking, you replace the pipe itself, by unscrewing the spigot from the pipe and the pipe from the Tee fitting below. Such short sections of threaded pipe are called pipe nipples, and can be had in many different lengths from any hardware or plumbing supplier.
If it's leaking from the threads you may be able to stop the leak by tightening the pipe to whichever fitting joint is leaking, or by removing it, reapplying thread sealant (either tape or pipe dope) and reinstalling it.
If the pipe cracked because it froze, you might need to take preventative action to keep it from freezing again, as it is clearly just exposed to the outside air in a manner not suited to anywhere the temperatures ever drop below freezing.