These key passages about the Resol'nare can be found in the source material. Note that formatting was not retained from the original material.
The Resol'nare given in Star Wars Insider #86 (Traviss, February 2006) is:
Mando’ade regard the following six acts — known as the Six Actions, or Resol’Nare — as central to Mandalorian identity: wearing armor, speaking the Mandalorian language, defending themselves and their families, raising their children as Mandalorians, contributing to the clan’s welfare, and rallying to the Mand’alor when called to arms. Anyone who practices them is considered a Mando'ad. The emphasis on carrying out these acts daily, not simply playing lip service to them.
Not directly about the Resol'nare, but potentially an insight into how the average Mando views following it. From Legacy of the Force: Sacrifice (Traviss, 2007), Boba Fett says:
You can't rule Mandalorians. You just make sensible suggestions they want to follow. ... And since when have Mandalorians needed to be told what makes sense?
The speaker of this statement is either being cheeky or there is more to the in-universe Resol’nare than a couple of lines found in an article or reduced to a rhyme. From Legacy of the Force: Sacrifice (Traviss, 2007):
Go read the Resol'nare. The six basic tenets of being a Mando. One is to rally to the Mandalore when called.
The Resol'nare rhyme in Order 66, opening of chapter 2 (Traviss, 2008):
Ba'jur bal beskar'gam, Ara'nov, aliit, Mando'a bal Mand'alor — An vencuyan mhi.
Education and armor, Self-defense, our tribe, Our language and our leader — All help us survive.
About wearing the armor, from Order 66 (Traviss, 2008):
There are two reasons why we have to wear armor. One is so that we don't get killed too easily. The other is so that we all look Mandalorian, however different we may be from our brothers and sisters.
One pertinent but vague statement by Kal Skirata, from 501st (Traviss, 2009):
The resol’nare, the six tenets of Mandalorian identity, said he was obliged to look after his kids, his clan, and his culture, and to rally to the Mand’alor in times of need.
From Knights of the Old Republic #26 comic series (Dark Horse, 2008, not by Traviss), spoken by a Neo-Crusader rally master to new recruits:
Once you were Dar'Manda . . . Ignorant outsiders. Those lives are over! You will raise your young as Mandalorians and defend them. You will wear our armor, and speak our language. And you will serve the clan, and rally when called. These are the Resol'nare, the Six Actions, sacred to our movement. Do them, and you may live to call yourselves Mandalorians!
Akaavi Spar dialogue in Star Wars: The Old Republic (game released in 2011; not by Traviss):
I adhere to the Resol'nare. The core of what it means to be Mandalorian. A sacred law giving us direction and purpose. Education and armor, self-defense, our tribe, our language, our leader — all help us survive. We must educate our children as Mandalorians, obey the commands of Mandalore, speak Mando'a and defend our clans.
Torian Cadera dialogue in Star Wars: The Old Republic (game released in 2011; not by Traviss):
Resol’nare means “Six Actions.” The core of Mandalorian life. Speaking the language is a big one.
The Resol'nare of the Death Watch, as presented in The Bounty Hunter Code (2013; not by Traviss) is:
Their teachings became the Resol'nare, the Six Actions that make us Mandalorians: raising the young to seek honor and glory, wearing armor, defending one's self and one's family, supporting one's clan, speaking a common language, and owing fealty to the leader of the clans.
Wanting to follow the Resol'nare requires a certain mindset. Here are some relevant quotes about it.
From Triple Zero (Traviss, 2006):
Mandalorians are surprisingly unconcerned with biological lineage. Their definition of offspring or parent is more by relationship than birth: adoption is extremely common, and it’s not unusual for soldiers to take war orphans as their sons or daughters if they impress them with their aggression and tenacity. They also seem tolerant of marital infidelity during long separations, as long as any child resulting from it is raised by them. Mandalorians define themselves by culture and behavior alone. It is an affinity with key expressions of this culture—loyalty, strong self-identity, emphasis on physical endurance and discipline—that causes some ethnic groups such as those of Concord Dawn in particular to gravitate toward Mandalorian communities, thereby reinforcing a common set of genes derived from a wide range of populations. The instinct to be a protective parent is especially dominant. They have accidentally bred a family-oriented warrior population, and continue to reinforce it by absorbing like-minded individuals and groups.
A speech attributed to a Mand’alor, which offers an overview of the in-universe Mandalorian mentality. From 501st (Traviss, 2009):
Here's why you can't exterminate us, aruetii. We're not huddled in one place—we span the galaxy. We need no lords or leaders—so you can't destroy our command. We can live without technology—so we can fight with our bare hands. We have no species or bloodline—so we can rebuild our ranks with others who want to join us. We're more than just a people or an army, aruetii. We're a culture. We're an idea. And you can't kill ideas—but we certainly can kill you.
From Knights of the Old Republic 2: The Sith Lords (Obsidian Entertainment, 2004; well before Traviss), Mandalore Canderous Ordo says:
As long as one Mandalorian lives, we will survive. Our honor, fortunes, and lives revolve around battle. From our earliest history, this has been our way, as it will be, always.
From Star Wars Insider #80 (January 2005), written by Abel G. Pena over a year before Traviss wrote the articles in Star Wars Insider #86. It would not surprise me to find out that Traviss either never read this, or did and retconned whatever did not fit the stories Traviss wanted to tell.
The Mandalorian shock troopers have undergone many permutations. The oldest documented incarnation is the Mandalorian Crusaders from around 4000-5000 years BBY. Made up of the clans of simianlike humanoids, these nomads roamed space seeking conflict, following a code called the Canons of Honor. The Canons aimed at helping warriors attain personal glory via combat and loyalty to one's clan. Despite this simplistic aim, the Crusaders were scarcely primitive, placing highest priority on plundering cutting edge weaponry at every opportunity.
The label of Mandalorian Crusader is misleading. It's thought that the Crusaders' forefathers were a religious warrior society with sophisticated laws that devolved into the cannons. But following the Mandalorians' epic clashes with the insectoids of Nevoota, war, once a ritual form of worship to Mandalorian gods, became itself devine and reverential. Henceforth, any campaign promising holy carnage was regarded a "crusade."