If you don't fancy exploring Starfield solo, you'll quickly get access to a few companions via the game's main quest, but there are people all over the galaxy just waiting for a captain to add them to their crew. This includes historical celebrity Amelia Earhart, the first female pilot to make a solo flight across the Atlantic. She went missing in 1937, but she's alive and well in 2330. Well, her clone is, at least. And you can recruit her by completing the Operation Starseed quest.
Starting Operation Starseed requires you to travel to Charybdis III in the Charybdis system. You'll receive a distress call that sends you there, but you can also visit it whenever you want—as long as your ship is up to the task. It's a level 65 system, and to reach it you might need to upgrade your ship's grav drive or just buy a new one. To fly the appropriate vessel, you'll also need a level 3 Piloting skill. The high level might make you think you'll have to wait until the end of the game before you can check this quest out, but I found it fairly manageable in the mid-30s.
Arriving in Crucible
Once you reach Charybdis III, you can land near the settlement, Crucible, where you'll be greeted by Tobias, a robot. An activity to give Tobias some resources will appear, but you can safely ignore it if you just want to focus on Operation Starseed. You'll be interrupted by Ada, the only human hanging around outside. Everyone's hiding inside their homes, she explains, but then directs you to speak to one of Crucible's leaders, Franklin.
Franklin, you'll quickly discover, is a clone of US President Franklin D. Roosevelt, and Crucible is full of clones of historical figures. It turns out that these clones are trapped on Crucible, and they've splintered into three factions, each with a different plan on how to deal with their predicament. FDR runs the Pragmatists, who believe that the clones should remain on Crucible until they are better prepared to live in the Settled Systems. Genghis Khan leads the Renegades, who will do anything to escape to the stars. Amanirenas is in charge of the Believers, who want to prove themselves worthy so that they can usher in a Golden Age across the known galaxy.
Other clones of historical celebrities include Ada Lovelace, who you met before, Wyatt Earp, who can sell you aid items and rent you a room, and Amelia Earhart, who wants to explore the stars. Once you've had a chat with everyone you can head back to FDR, who will ask you to go to the Facility. No matter which of the factions you eventually decide to side with, the Facility will be key to their plans. It's breaking down, you see, and FDR wants to control it so he can use it to make Crucible a more functional settlement, while Amanirenas wants to reactivate it so the Believers can continue the project's original mission. Genghis Khan, meanwhile, simply wants to destroy it so he can be free. First, though, you'll need to make a quick detour.
Wyatt Earp's request
Before you head off to the Facility, Wyatt Earp wants to talk with you in secret, suggesting that he knows something terrible about FDR. After all, you can never trust a politician. You'll need to meet him in a cave near Crucible.
When you arrive, he'll come clean: this was all a ruse and he's not actually Wyatt Earp. He's the clone of notorious serial killer H.H. Holmes. Believing that you would discover his true identity, and fearing what the other clones would do if they found out, he threatens to kill you.
If you have the Persuasion skill, it's possible to avoid a fight here. You can talk him down and promise not to tell anyone who he really is, after which he'll return to Crucible and continue to pretend to be Wyatt Earp. After this, it's still possible to inform the clones about his real identity.
You'll need to hop back into your ship to travel to the Facility, since it's far from Crucible, though still on Charybdis III. Unfortunately, the building now has some new residents: maggotmaws. The place is full of them, and you'll want to take them out before they get close because they're rather adept at ripping humans to shreds.
To complete this stage of Operation Starseed, all you need to do is find seven slates that detail what happened in the Facility before the clones left and established Crucible. Each slate has a quest marker, so they are easy to find. The biggest threat in the Facility is the maggotmaw boss, who you'll naturally meet near the end of this section. Keep your distance, pop down some mines and try to keep your companion between it and you, and you should be fine.
Eventually, you'll reach the entrance to the restricted area, but unfortunately, there's no way to access it at this point. Instead, you'll need to head back to Crucible and give the clues you discovered to the faction you want to side with, before hunting down the security override code.
Finding the Beagle
It turns out the Facility was once a ship, and its sister ship, the Beagle—no doubt named after the vessel made famous by Charles Darwin—should have the code needed to progress further into the Facility. Thankfully, Ada Lovelace will be able to tell you where to start looking.
First, you'll need to head to Bel V, and then from there travel to Zelanzy I, where you'll be able to board the Beagle. The crew is dead, but there are still some security measures to deal with. Once you've found the codes, you can then zip back to Crucible. When you get into orbit, however, you'll get a message telling you there's an emergency. Travel down to the planet to attend a meeting between the leaders.
The two leaders you didn't give the slates to have found out and are not best pleased, so you'll need to deal with a stand-off. It's possible to talk one of them down, but a fight still appears to be inevitable. Once you kill the opposition leader, you can loot their corpse for a unique outfit. Now you can give the code to Ada Lovelace, who will decrypt it, allowing you to go back to the Facility and finish things.
Returning to the Facility
In the restricted area, you'll have to contend with lots of automated turrets and clone guards. Expect to be attacked from above and below as you make your way through it.
At the end of the Facility, climb up the stairs and into the main control room, where you'll find the computer that lets you determine who gets control over the Facility. Once you do that, you'll be locked out of the computer, completing your business here.
Next to this room is a locked door that you'll want to investigate, since you'll find some pricey loot. Harvested organs might not sound like something you want to cram into your pocket, but they'll make you a nice chunk of cash. This is considered contraband, however, so you'll either want to have some shielded cargo space, a device that lets you avoid scans, or stick the organs in an outpost cargo container before you hit your next settled world.
Recruiting Amelia Earhart
Now that you've dealt with the Facility, you can return to Crucible and get your reward: some cash and a new companion. The leader you sided with will thank you and fill your bank account—no, I have no idea how a bunch of isolated clones have so much money either—and then you should go and have a chat with Amelia Earhart.
She's now able to join your crew permanently and has a level 2 Piloting skill and a level 2 Rifle Certification skill. So she's not nearly as skilled as your story companions, but to be fair she's a clone of a 400-year-old pilot who's never left her prison planet. But she's still worth recruiting just for the novelty of getting to hang out with a celebrity.