Beginning this side quest will require you to visit the NCR Sharecropper Farms, an (obviously) NCR-controlled location south of Freeside and the New Vegas Strip. Gun Runners is directly to the north of it. When you arrive at this expansive area, you'll find some farms that the NCR uses to grow fresh food for their troops. The fields are irrigated with fresh water, and seem to be thriving, both outdoors and inside makeshift greenhouses. The person you want to speak with here to get things moving is a woman named Morgan Blake. While you may find her roaming around the farm itself, chances are you'll actually end up locating her in the barracks on the premises. She won't speak to you at length when you talk to her, but you can offer to help her investigate a problem with the irrigation at the farm, at which point you'll receive this side quest.
The location you need to travel to presently is actually fairly easy to find. It's due east only a short distance from the Sharecropper Farm. This locale, known as the East Pump Station, is the first place you're going to have to travel to in order to ultimately fix the problem at hand. Head into the East Pump Station, and you'll find yourself immediately inside of a small office. On a desk at the far end of the small office is a computer. The computer functions, but a moderate Science skill will be required to fix something on the computer so that you can continue to learn what the problem is. When you explore the contents of the computer thereafter, you'll learn that the origins of the issue are at Vault 34.
Thankfully, just like the Sharecropper Farm and East Pump Station are situated next to each other, so too is the East Pump Station and Vault 34. Vault 34 is located southeast from the station, and you can get there easily enough by walking (though you can quick-travel there, too, if you've already been there). The entrance to the Vault is a little foreboding, since there's radioactive goop and a barrel in front of it. This is a sign of what's inside, because much of Vault 34 and its outlying areas are also heavily irradiated. It won't hurt to have some Rad-X and RadAway on you here. Inside, you won't immediately arrive at the Vault's front entrance. You'll need to walk down a linear, irradiated cavernous pathway first. Radiation is everywhere, as are Golden Geckos, so have your weapon-of-choice at the ready.
Once you arrive at the vault itself, we'll get down to the nitty-gritty. At Vault 34, the enemies you'll be fighting aren't Golden Geckos, but rather Ghouls, heavily irradiated by any number of nearby subterranean substances. Your trip here can be as long or as short as you want it to be. Vault 34 has its own interesting story to tell, since many of its ghoulish inhabitants were once human (just like all Ghouls, in fact). Exploring Vault 34 in its entirety and delving further into its story is entirely optional for you, and won't be covered here. What we're really at Vault 34 for is to do one thing, and that's to get the water flowing to the NCR crops once more, free of pesky radiation.
The general idea once inside Vault 34 is to work your way lower and lower through the various floors and tiers of the vault. As you explore, expect to run into a plethora of Ghouls of varying strengths. You'll also no doubt notice that you're constantly being irradiated once down here, and without the best-of-the-best anti-radiation suits, you won't really be able to do anything about it. As we mentioned earlier when you were in the equally-irradiated tunnels leading to Vault 34, you'll want to be absolutely certain that you have Rad-X activated on you at all times, and that you have plenty of RadAway to get rid of radiation poisoning as it slowly builds up. Also, it's worth noting that there are quite a few medical kits in the dark corners of Vault 34, should you need to raid them to bolster your curative item stock.
There are a few important things to keep an eye out for as you move through Vault 34. The Vault 34 Utility Terminal Password and Vault 34 Security Terminal Password are two codes in particular that you'll need to pick up. Doing so will require you to venture into the flooded, aqueous depths of the vault, where a code can be found on a dead Ghoul body. Ultimately, new codes will allow you to access locked computers and doors that will bring you to the Overseer's Office of Vault 34. But if you expected it to be abandoned, think again. Not only are a couple of gun turrets adamantly guarding the door, but the Ghoulish Overseer is also still in his office. Kill him, grab the password off of his body, and then use the computer at the back end of his office to unlock a new door further down into Vault 34.