The jobs are grouped by where you go to do them. There's a table with the following information in each section:

Job Name: What it's called.
Primary Skill: This is the first skill doing the job raises, and is the skill that receives the bonuses from cards, gear, successfully completing the job, and hitting the super goal, as well as any boosts from modifications Sol has.
Secondary Skill: If the job boosts a second skill, it's listed here. This skill only gets a bonus if Sol has a relevant modification, and isn't affected by cards, winning, or super goals.
Friendship: Doing this Job raises Friendship with this character - usually one, but some cases will have two.
Kudos: How much Kudos (if any) you earn for doing the job.
Stress: How much Stress you accumulate for doing the job.

After the table is a list that talks about how to unlock each job, with varying levels of detail.

At the end, I've also included a section that breaks down where you should get Sol to do if you're aiming to raise a particular skill, and another one if you're trying to get them to befriend someone. Note that the skill section only talks about specific jobs - there will be dialogue options with friends that can alter skills as well.

Deliver Supplies: Requires 10 Organising or 10 Toughness; Marz will mention it during Quiet of the first year if Sol talks to her/goes and gets the soysweets from Tammy that she asks for.
Work in the Depot: Requires 20 Friendship with Marz; talking to Marz after Sol turns 11 will eventually unlock this.
Work Construction: Once the Heliopause crash-lands, doing any job in Administration will trigger a random event with Rex where he lures Sol off to help with construction, unlocking the job.
Assist the Governor: Requires 60 Persuasion or 29 or lower Rebellion; once the Heliopause crash-lands, doing any job in Administration will trigger an argument between Lum and Seeq, which will make this unlock available.
Govern the Colony: Requires overthrowing Lum and getting Sol voted in as governor:

1. During a meeting of the Secret Funtimes Club in Sol's 17th year, Marz will raise a complaint about Lum and decide that he needs to be overthrown. Sol can either support Marz or throw their hat in (which requires about 80 Persuasion).
   
2. Either way, Sol needs to speak to all six Council members - Seeq (and Eudicot if she's alive), Auntie Seedent, Flulu, Utopia, Instance, and Rhett - to get their support.
   • Auntie Seedent will only give her support if Sol's gathered at least three other votes already, but she doesn't need a check.
     
   • The other Council members will need successful Persuasion checks to convince; if Eudicot is alive Sol doesn't need to make a check for Seeq.
3. During the next Vertumnalia (when Sol is 18), Marz will storm the stage and start the coup process, at which point Sol needs to step up and offer themselves as a replacement. If they got all six votes in time, they get sworn in as Governor.

Study Life Sciences: Always available.
Study Humanities: Speak to Geranium (Sol's Dad) once they emerge from medbay at the start of the game.
Study Engineering: Requires 5 Reasoning; the unlock becomes available after studying once.
Tutor Children: Requires 30 Reasoning; will become available after studying several times.
Repair Robots: Requires 50 Engineering; becomes available in a random event after the Heliopause lands, triggered by going to do something in Engineering.
Assist in Medbay: Requires 50 Biology; becomes available in a random event after the Heliopause lands, triggered by going to do something in Engineering.
Rebuild and Mourn: Only available for the two months after the Faceless attack in the fourth Glow.

Explore Nearby: Can be unlocked as early as age 10:

• 10 Friendship with Dys: Tangent will ask Sol to find out where Dys goes; speak to Dys and he will show Sol the way out.
  
• 20 Toughness or 20 Bravery: Speak to Tonin/Utopia at the front gate; once they rebuff Sol, Dys will get their attention and show them how to sneak out.
  
• Automatically unlocked on Sol's 13th birthday.

Survey the Plains: Automatically unlocked on Sol's 13th birthday.
Forage in the Valley: Automatically unlocked during Quiet of Sol's 14th year.
Survey the Ridge: Requires Perception 30: While exploring the Plains, Sol may get an event at the start where they can try and track down a mysterious thumping noise. Succeeding on a Perception check locates the thumper and unlocks this.
Hunt in the Swamps: Once the Heliopause crash-lands, an option can come up either visiting the garrison or going on an expedition; this will involve passing an Animals or Combat challenge, and success will unlock this option.
Explore Glow: Requires a specific sequence of events:

1. While Surveying the Ridge, there's a "boss event" at the end that, if passed, will reveal the location of a Collector city.
   
2. A second boss event that involves discovering the Relay can also be triggered - either after discovering the city, or as a Boss event while Foraging in the Plains.
   
3. Once Sol's found the Relay, they can trigger a deeper exploration of the city. This will require being fully rested and either 50 Toughness or 50 Reasoning and passing a Toughness or Reasoning check. If successful, this will give Sol a deeper insight into the Relay and the wormhole, and unlock this option.

Play Sportsball: Unlocked in the second month of Quiet after Sol talks to Anemone.
Defense Training: Automatically unlocked on Sol's 11th birthday.
Lookout Duty: Requires 20 Perception; after Sol turns 11, going to the Garrison can randomly trigger an event with Rhett that makes the unlock available.
Guard Duty: Requires 30 Combat and 10 Bravery; Once the Heliopause crash-lands, going to the Garrison can randomly trigger an event with Rhett and Vace that makes the unlock available.
Relax on the Walls: Automatically made available when Sol is 11, during Vertumnalia.

Shovel Dirt: Unlocked automatically after finishing the first month.
Work on the Farm: A random conversation with Flulu triggered by working in Geoponics once Sol hits age 11.
Research Xenobotany: Unlocked once Sol gets 35 Biology.
Tend the Animals: Requires 20 Animals; unlocked by a random conversation with Geranium triggered by working in Geoponics once Sol hits age 11.
Relax in the Park: Unlocked by a random conversation with Cal triggered by working in Geoponics once Sol hits age 12.

Babysitting: Sol has to save Tammy's life in Early Pollen of Year 10; talk to Tammy the next month and the job becomes available. Note that this Job is only available during the first four years.
Help in the Kitchens: Requires 20 Organising; Auntie Seedent offers it during a random event in the Living Quarters, as early as 11 years old.
Work in the Cafe: Requires Friendship 50+ with Rex; Sol needs to give him mushwood logs (around 5-10) after Rex tells Sol about his plans for opening a bar.
Practice Photophonor: Requires a photophonor; you can either get one as Sol's twelfth birthday present or purchase one in the store when it becomes available (which I think requires 35 Creative for the first Perk).
Relax in the Lounge: Always available.

• Assist in Medbay (+3, Primary)
  
• Work in the Cafe (+3, Primary)
  
• Babysitting in the Creche (+2, Primary)
  
• Help in the Kitchens (+2, Secondary)
  
• Tend the Animals (+2, Secondary)
  
• Tutor Children (+1, Secondary)

• Assist the Governor (+3, Primary)
  
• Govern the Colony (+3, Primary)
  
• Study Humanities (+2, Secondary)
  
• Work in the Depot (+2, Secondary)

• Practice Photophonor (+3, Primary)
  
• Help in the Kitchens (+2, Primary)
  
• Study Humanities (+2, Primary)
  
• Work in the Cafe (+3, secondary)
  
• Repair Robots (+2, secondary)
  
• Babysitting in the Creche (+1, secondary)

• Explore Glow (+2, Primary)
  
• Explore Nearby (+2, Primary)
  
• Play Sportsball (+2, Primary)
  
• Govern the Colony (+3, Secondary)
  
• Guard Duty (+2, Secondary)
  
• Practice Photophonor (+1, Secondary)

• Tutor Children (+3, Primary)
  
• Study Engineering (+2, Secondary)
  
• Study Life Sciences (+1, Secondary)

• Deliver Supplies (+2, Primary)
  
• Work in the Depot (+2, Primary)
  
• Assist the Governor (+3, Secondary)
  
• Rebuild (+3, Secondary)
  
• Research Xenobotany (+2, Secondary)

• Repair Robots (+3, Primary)
  
• Work Construction (+3, Primary)
  
• Study Engineering (+1, Primary)
  
• Survey the Ridge (+2, Secondary)

• Assist in Medbay (+3, Primary)
  
• Research Xenobotany (+2, Primary)
  
• Study Life Sciences (+2, Primary)
  
• Work on the Farm (+2, Primary)
  
• Forage in the Valley (+2, Secondary)

• Rebuild (+3, Primary)
  
• Shovel Dirt (+3, Primary)
  
• Work Construction (+2, Secondary)
  
• Work on the Farm (+2, Secondary)
  
• Play Sportsball (+1, Secondary)

• Lookout Duty (+3, Primary)
  
• Survey the Plains (+3, Primary)
  
• Forage in the Valley (+2, Primary)
  
• Survey the Ridge (+2, Primary)
  
• Deliver Supplies (+1, Secondary)
  
• Explore Glow (+1, Secondary)
  
• Explore Nearby (+1, Secondary)

• Guard Duty (+3, Primary)
  
• Defense Training (+2, Primary)
  
• Hunt in the Swamps (+2, Secondary)

• Tend the Animals (+3, Primary)
  
• Hunt in the Swamps (+3, Primary)
  
• Defense Training (+1, Secondary)
  
• Lookout Duty (+1, Secondary)
  
• Survey the Plains (+1, Secondary)

• Defense Training
  
• Lookout Duty
  
• Play Sportsball

• Research Xenobotany
  
• Shovel Dirt
  
• Tend the Animals
  
• Work on the Farm

• Explore Nearby
  
• Survey the Plains
  
• Forage in the Valley
  
• Relax on the Walls
  
• Survey the Ridge

• Assist the Governor
  
• Deliver Supplies
  
• Govern the Colony
  
• Work in the Depot

• Practice Photophonor
  
• Repair Robots
  
• Study Engineering
  
• Tutor Children

• Deliver Supplies
  
• Relax in the Lounge
  
• Work Construction

• Babysitting in the Creche
  
• Help in the Kitchens
  
• Relax in the Lounge

• Assist in Medbay
  
• Study Engineering
  
• Study Humanities
  
• Study Life Sciences
  
• Work in the Cafe

• Defense Training
  
• Guard Duty
  
• Hunt in the Swamps