The Official Route
Documentation
When the colony of Persephone was founded, each of the powers were highly particular about the calibre of colonists they accepted. The original three colony ships were filled with what was perceived as the cream of the crop, and subsequent would-be colonists were rigorously screened for suitability. Space, it was universally acknowledged, wasn't for everyone, and letting the wrong sorts into the embryonic colony could lead to catastrophe.
From the start, though, there were problems. The United Nations controlled all aspects of passenger transport, but the United Nations is a conglomeration of nations with different laws and different priorities backed by largely unfireable government bureaucrats and corporate interests whose goals did not always line up with the UN's. As a result, the screening process was far from airtight, and after the particular care given to the first three colony ships, it was no real trick for an unsuitable candidate to slip aboard a transport. Spaces were so limited that once an unsuitable candidate was found planetside, the colonial administration couldn't dream of affording to send them all back - particularly since the countries of origin usually didn't miss them anyway.
A thriving market appeared in all urban centres of black-market papers and travel certificates, granting the bearer access to a Persephone transport if they could cough up the money for a ticket. Some worked, gambled, or stole to get what they needed. Some simply skipped the whole process and stowed away. At first, United Nations Security Force soldiers were detailed to each transport with live weapons and authorisation to shoot to kill to try and deter stow-aways. But when the porousness of the screening systems became clear, most of the authorities stopped pretending to do anything but the most cursory glances.
The only group in any real danger were those who could not be permitted to leave their home nations: political prisoners, major criminals, and the like. In these cases, if discovered on Persephone the offender would usually be shipped back at the home nation's expense. But even these undesireables, once planetside, could find it easy to blend in.
The Process
Three large United Nations-owned passenger transports ply the spacelanes between Persephone and Earth. They each stop at one boarding point: the SV Golden Sun stops in Beijing?, the SV Revolution in Mexico City?, and the SV Red Dawn in Brussels?. There are also smaller, private vessels which have authorisation to carry passengers; routes and schedules for these vary.
The cheapest ticket on a United Nations liner can cost as much as a year's salary for a labourer in an industrialised country, and entitles the bearer to a simple seat on the week-long journey between Earth, Alpha Centauri, and Persephone. Those with pre-arranged employment in Persephone often arrange plans with their employers where the cost of the ticket is deducted from their salaries. Private transports are typically more expensive, and private berths on any vessel are the preserves of only the wealthy.
The trip between Earth and Persephone takes one week, barring misadventure. The bulk of this time is spent at sub-light speeds, moving to the Sol jump gate leading to the Alpha Centauri system, then through Alpha Centauri to the next jumpgate leading to the Epsilon Indi system, and from there to the actual planet. The vast main drives on the United Nations transports propel the transports up to an estimated top speed of three-fifths the speed of light.
The Journey
First-class cabins are available on all three United Nations transports, and for those who inhabit them it is one of the most luxurious journeys in the galaxy. Impeccably tailored servants are on call at every hour of the artifical day. Vast observation lounges allow spectacular views of space. Cuisine is provided by Michelin-starred chefs operating in state-of-the-art kitchens, and the Red Dawn in particular is known for the quality of its table, having been called "the best restaurant off Earth" by top critics.
Even in second class, the journey can be marvelous. Cabins are small but they are located along the hull, with big windows staring into space. Meal sittings occur in tastefully appointed dining halls and the menu, while small, is delightful. Modest common areas allow sociable travellers to meet their fellow voyagers, and staterooms can be rented for group meetings.
The bulk of passengers will travel in steerage, and there conditions are not so good. On initial journeys, standards were set high but the operators complained about the meagre profits and persuaded the United Nations to reduce the number of restrictions. Passengers are stuffed into every available space, and though in theory a ticket entitles every passenger to a seat there are more tickets sold than seats available. Luggage is highly restricted, and more than one family has had to abandon their goods forever. Service is literally non-existant aside from company stores charging intolerable prices for food and water. Once the ship launches, it's not as though a passenger can get fed up, get off, and walk the rest of the way, and the company knows it.
When the transports arrive at Persephone, most passengers are only too eager to leave.
Unofficial Travel
Officially, immigrants to Persephone are only permitted to take a United Nations-approved transport, including one from a private operator. These operators are required to maintain certain standards of security and safety, and the ticket prices reflect this.
Unofficially, many passengers with no alternatives take other routes to the colony. The most frequent way is to secretly buy passage on a cargo ship. Usually stuffed into a sealed cargo container with a modest air supply, some food and water, the passengers are loaded into airless and unpressurised cargo holds and endure an agonising journey between Earth and Persephone. The sealed container prevents instant death from exposure to vacuum, but with passengers usually stuffed from wall to wall and various complications from space travel common, the experience can be brutal. Worse, the sorts of delays common in freight shipping - queues at jump gates, delays in getting takeoff or landing clearance, delays in cargo processing, and the like - can lead to mass fatalities among underprepared voyagers. But it is cheap.
In early days of the colony, those with money but various factors preventing them from getting official passage sometimes got more inventive. Human interstellar vessels were too expensive and too few for easy smuggling, so these escapees would be taken into orbit on an intra-system vessel like those used to move between Earth and Mars, where the vessel would covertly meet with an alien ship away from the prying eyes of human officials. Alien vessels are prohibited in the Sol system, so this ship would have to very carefully arrange its trip to Persephone or risk impounding, including circuitous jumps meant to evade human patrols, fraudulent registrations and manifests at jump gates, and bribery. This journey was comfortable, if long, but has largely fallen out of favour for all but the most toxic prisoners of their own state.