The book of Love: Opens up after the first house is done.
- Basically you just need to make Adahy and Elu fall in love and have kids.

Name the New Born Nuggets: The first two kids are born.
-Just name the kids

Backbreaking Work: Two new nuggets get married and try to make a house
-grab up stone and wood and give it to the house so the nuggets can build.

Broken Heart: you need to break up a couple using the Le Cupion power.
-Kill the target that the nugget is directing their rage at.

Dead Nugget: This one will only start when you have a staffed graveyard built and someone dies
-Move the body to a graveyard
-Alternatively you can use healing on the body to give your gravedigger time to get it.

Find my Lost Nugget: Pops up after enough houses are built and enough families and couples are present.
-You just need to find the missing child. A good way to do this is to locate them in the house panel.

Heal a Nugget: Happens when a nugget gets sick from any source
-You can heal the nugget afflicted with illness using your powers.

Food Discovery: Starts up when you have researched and placed a farm
-Search around for any wild plants and pick up the fruits, then toss it on the farm.

Tesla's Quandry: This one is required to progress, so you'll get it eventually once electricity is discovered.
-First you need to build a battery
-Next you need to find the broken parts and toss them onto the battery in construction
-Finally you need to strike the battery with lightning to charge it some.

Gone Green: I've heard conflicting reports on this one, some say you need to get eco below 60%, but i've had it happene at 80% and below. You can drain water and remove trees to get there quicker.
-You basically need to use Forestation to place a large swath of trees somewhere.

Put out the house fire: Once you have Material Refining researched, you just need to wait till a house has caught on fire. I've found building some refineries for wood and stone tends to take enough time for it to happen
-Douse the fire with the Trickle Effect power. You get the Fire creator power doing this one.

Lake Cleansing: Triggers when a lake has gone toxic
-Simply clean the lake by using the Trickle Effect Power

The Last Exhibitionist: Comes up a bit after researching Clothes
-Switch the season to Winter so that the offending Nugget is forced to put on clothes

The Nugget's Fierce Enemy: Starts after you've researched Lumber Mills
-Your first task is to build a lumber mill somewhere. They're particularly big so have space
-Your second task is to cut down a LOT of trees in an area marked with a circle.

Overpacked: Starts when you've researched Couriers
-Your first task is to palce a courier hut somewhere.
-Afterwards you simply need to deliver a few packages yourself to some mailboxes that spring up in town.

Sitting on Powder: Research Gunpowder, then wait for a new leader election
-This one is a little confusing. People say you need to ignore the quest and kill the quest giver, but that may have been an older version. What I've found is that you just need to vote the chosen nugget candidate into office. If at that point it doesn't complete, then just kill the quest giver.

The Root of the Problem: a few minutes after you research mining, this quest should pop up.
-A large vine will pop up near your evolution tower. You need to smite it with lightning a few times
-Once the vine is gone, you need to build an expedition camp on the hole it left.

Pursued by Bear: I THINK this one triggers if you've got a garrison and are in the stone age with a few traps out.

Friend or Foe: Not sure what triggers this one, but the fact 'spear' is part of it may mean its stone age exclusive.

Power Hour: This one obviously happens some time after electricity has been discovered.

It's not murder if there's a party: Again, not sure what this one triggered by, i'll get back to you on it.

Spider Infestation: This one is somewhere between medeival and modern ages, and depends on how many warehouses you have I think

Artisanal Artery Clogging: This one has to be somewhere in the modern age, likely with the advent of modern age eatery upgrades.