Long Distance can start in one of two ways - immediately after completing The Demolished Woman and talking to Akande, or after completing The City and the Stars, where you'll be contacted by Akande when you return to the Unreliable. In the latter case you have to be following Phineas' questline through the game and have ignored quests like Balance Due and its following quests, The Puppet Masters and The Demolished Woman, which will become inaccessible if you haven't resolved them before starting The City and the Stars. Suffice to say, if you're working with Phineas, this quest will occur much later in the game than if you're working for the Board.
The Meaningless Bug
In any event, you'll be asked to give up Phineas' location by bugging the communications terminal in his lab. There's no trick to this, just walk in, head to the communications terminal west of Phineas' enclosure and pick the option [Send Tracking Signal]. It's really that simple. On the other hand, you can talk to Phineas and reveal Akande's plot by saying "The Adjutant asked me to plant a tracking signal in your lab, but I'm not going to do it.". Surprisingly, Phineas will encourage you to plant it, albeit with a corrupted signal, which will both convince Akande you're a loyal minion and buy Phineas some time. You can do this by activating the aforementioned communications terminal and picking the option [Send Corrupted Tracking Signal].
Even more surprising than Phineas' response is how little this decision actually matters. Planting the bug - corrupted or not - will not prevent you from siding with either Phineas or Akande in the long run, and in fact, events will play out identically either way. The point of no return when it comes to picking your allegiance in the main questline is a single dialogue decision a bit later on (if you're following Phineas' questline) or much later on (if you're working for the Board or playing both sides). So, seriously, do what you wish, and even if you want to keep your options open (in other words, play both sides) you can freely return to Akande and keep working for her without burning any bridges with Phineas.
Note: Your negative reputation with the Board, if any, will be reduced after bugging (or faux bugging) Phineas' communications terminal, which may be necessary depending on your previous actions... especially if you're starting this quest after The City and the Stars.
Meeting Adjutant Akande (Again?)
Depending on where you are in the story, the way this quest ends will vary. If you have not completed The City and the Stars yet (in other words, you're following the Board path inasmuch as you've completed Balance Due, The Puppet Masters and The Demolished Woman) you'll be invited to meet with Akande in Byzantium, which by now is rather mundane. On the other hand if you did complete The City and the Stars you'll finally gain access to Adjutant Akande's Landing Pad in Byzantium, which should be your next destination.
If you haven't visited Adjutant Akande's Landing Pad before, the next bit of Long Distance will play out similarly to the start of The Puppet Masters. Make your way west off the landing pad and go through a doorway to reach the HHC Building, stopping at a checkpoint so one Guard Esparza can check your papers. Continue west when she's done and go through another door between two corporate troopers to reach a room with two vending machines. Peruse them if you wish, then head up an elevator to the south.
When the elevator arrives you'll find yourself on the third floor of the HHC, the northern end of which is dominated by the desk of Percival Platt, whom you've no need to talk with at this time. This place should be familiar if you've completed The City and the Stars, of course, and even moreso if you've been working for Akande a while. Regardless, you can now talk to Akande in person, instead of remotely through a screen, so go through the door to the east of Platt's desk and chat with Akande.
After she questions you about your motivations for turning in Phineas she'll get back to business, and this quest plays out different depending on where you are in the story. If you've been following the Board questline (which is also the guide's suggested path, although we're technically still playing both sides) after previously completing Balance Due, The Puppet Masters and The Demolished Woman, continue with the text under the header "Muting Monarch", which ironically may advance Phineas' questline... If you're meeting Akande after The City and the Stars, however, read the text under the header "Downsizing the Workforce", which may vary depending on your earlier actions in the game.
If you're starting this quest after The Demolished Woman she'll tell you that she wants some broadcasts on Monarch shut down, which requires you to travel to the Devil's Peak Station. As for where this actually is located and how to get there, she'll suggest you talk to one of her agents in Stellar Bay, Everett Gill, and give him the passphrase "the kindapine grows at night". You can pass an [Intelligence] check to identify this as the name of a romance serial (when did your protagonist have the time to figure that out?), which is one of the few humanizing moments Akande has in the game. In any event, you'll need to talk to Platt to get your reward and the Stellar Bay Navkey you need, after which Long Distance will finally end and you'll be able to safely proceed with Signal Point in Space. You can also now peruse some Board-exclusive gear by talking to Platt, which includes the unqiue weapons Pauper Popper and Latinus.
If you did not buy the Stellar Bay Navkey from Gladys yet for the quest Passage to Anywhere, the option to do so will now be lost. This saves you 10,000 Bits and does not botch the quest Passage to Anywhere, as you can now contact Phineas on the Unreliable and tell him you have a Stellar Bay Navkey - he's surprisingly incurious about where you got such a thing, but the details don't matter, so long as you can safely make your way to Monarch. In any event, he'll tell you that you need to find one Hiram Blythe, who should have the information you need. This starts the quest Radio Free Monarch, which is virtually identical to Signal Point in Space, and both will update simultaneously if you have both. You can even turn both in once completed without compromising your working relationship with either Akande or Phineas! That's right, the point of no return isn't Monarch, and really, there's no reason to not have both quests at the same time.
Either way, your next destination is Monarch, and it really doesn't matter much which of the two aforementioned quest pages you go to. They're both superquests that will require you to complete numerous side quests and faction quests, which are identical whether you're working for the Board or for Phineas, and again, both quests will update as you complete these objectives. The only real difference is where you seek out Nyoka first (Phineas' suggestion) or make contact with Akande's agent, Everett Gill... after which you'll need to talk to Nyoka anyways. No reason you can't talk to Everett Gill first, then Nyoka, regardless of where your loyalties lie.
Downsizing the Workforce
On the other hand, if you're here after The City and the Stars you may face an entirely different task, depending on your actions earlier in the game. If during Comes Now the Power you reroute power to the Botanical Lab or you put Adelaide in charge of Edgewater, Akande will demand that you... amputate the necrotic limb that is Edgewater from the colony. Fortunately you don't have to get your hands dirty yourself, you'll just need to sneak into the Geothermal Power Plant and get the automechanicals to do the dirty work for you, after which you'll need to scrap said automechanicals. This starts the quest Foundation, which must be completed before you can move on to Akande's next task.
Note: If you refuse to liquidate Emerald Vale, Akande and the rest of the corporate goons on the level will turn hostile. Suffice to say, this will effectively end the Board questline.
If you diverted the power to Edgewater and left Reed in power, however, you'll just gain some congratulations from Akande for your work in restoring prosperity to Edgewater, whose workers will now be given preferential treatment in Akande's plans. This earns you the somewhat elusive trophy/achievement, "Mightier than the Sword". More importantly, Akande will now tell you about her next scheme - she needs the Hope, and more specifically she needs you to skip the ship to Tartarus. This starts the quest Kept Secret But Not Forgotten.