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The Boomers - Getting into Nellis Air Force Base
The Boomers are hidden in the base to the northeast of the strip. Follow the railroad tracks and you should be able to find the entrance, marked with a bunch of pictures of dismembered bodies and lots of warnings.
As your quest giver should have mentioned, the Boomers got their name for a reason. They have the entire path to their base marked up for their big artillery pieces, and they've got plenty of ammo. If you linger in any one spot, you will get blown to pieces.
If you are playing in hardcore mode, amke sure that you send your companions back to the Lucky 38. They won't survive. Make sure that you're not wearing heavy armor or anything that slows you down. I would suggest bringing a hydra. You'll probably get a lot of limb damage from a close hit at some point. Being able to heal it quickly will be important. That, or be ready to burn through a few doctor bags or stimpaks.
When you're ready, enter the bombed out town and start running. I managed to do this successfully by running to the right side of the town. This involved a few unintuitive choices, like taking a small detour around a house, but by sticking close to the house walls on the right side, I seemed to not take too many hits. Don't just run in a straight line; It looks like they can lead their shots. Use diagonal lines and zig zag a bit to survive. Once you make it out of the town, you're home free. Get to the gate and talk to the guard. Agree to see Pearl to finish the running portion of the mission.
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Friendship with the Boomers - The Big Things
For starters, go to Raquel and ask about the ants in the building. The reason you want to do this quest first, is that it's only possible in this phase of “Volare!" It will be locked out once you prove yourself to the Boomers, and it has a lot of good equipment and a unique grenade launcher as the reward. Besides, it's the one combat mission and there's a potential for a lot of explosions. “Ant Misbehavin'" will get its own article though.
“Young Hearts" is a good one to do if you already have a marker for the Crimson Caravan company on your map. You basically just have to run back and forth a few times.
“Sunshine Boogie" is a great and potentially quick quest. Just talk to Loyal in his workshop. Their solar arrays are fairly wrecked, so they need someone to fix them. Anyone can fix the solar panels if they salvage parts from the Helios One solar array (from That Lucky Old Sun, you should really do that quest if you haven't yet). You're just salvaging broken panels that are marked in the yard, so no one cares. I believe you will need 35 points in Repair to salvage them though. You can use these parts to fix the panels without a Repair check. If you have Repair greater than 65, you can just optimize and fix the panels without any parts.
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Friendship with the Boomers - The Little Things
You can give scrap metal to Jack. He's usually in the hangar.
You can give missiles to Raquel after you finish “Ant Misbehavin'", although that's a fairly expensive option.
If you have more than 7 points in Charisma, you can be nice to the kids at the base and get little reputation boosts from that. You can also give them those rocket souvenirs from Novac. They'll love them (this is also why they're marked as quest items, I believe).
You can talk to one of the young girls, Lindsay, and agree to find Mr. Cuddles for her. The teddy bear is in the main hangar with the B-29, lying in a little alcove formed by a pile of crates. You can also pass a 60 point Speech check to tell her that Mr. Cuddles is dead, which nets you Boomer infamy, but is a nice option for evil players.
If you go to their museum and listen to the kid's tour, you should get a small boost to reputation. Plus it's a little funny and tells you what their long term plans are.
Once you get enough reputation, “Volare!" will update to have you talk to Pearl.