To what degree should the DM help the PCs construct this back ground?
The way I handle it is I tell the players about the world in a handout/email and in person about 2-4 weeks ahead of the first adventure, and let them ask me any questions they want, as long as they don't involve campaign secrets.
I generally let them know about major organizations, the races & classes available, what books I'll be using, etc.
If they come up with something I don't consider viable, then I let them know. Example: I posted in another thread a campaign idea in which the players all start as regular soldiers, mercenaries, or paid civilians in the service of a Regent who is the world's equivalent of Sauron (though they don't know it when the campaign starts), right before the other nations unleash their armies. As such, no one could reasonably
start the game playing a Paladin or something similar- such a person would be weeded out by the Regent's agents.
However, after that starting point, all decisions are in the hands of the PCs. Continue in the service of evil or rebel?
But the fact of the matter is: different players will need different amounts of help. In my current group, we've got one guy who is a Ranger junkie. Every PC I have seen him play in the past 10 years has been either an actual Ranger or extremely Rangeresque. The very generic-ness and interchangibility of his PCs makes it easy to slot them into any campaign.
On the other hand, another guy in the group is a very creative type, and his PCs are usually...
unusual (5 points if you guessed it was me). I'm always coming up with concepts in my backgrounds that my DMs yank. And I'm not the only one. I'll never forget the fun I had helping a player create a 1st level PC in one of my campaigns when he said to me "I want to play the Crow." That was a challenge...
And why are they all together anyway if they have created very diverse backgrounds?
That is campaign and game group specific.
The last time I started a campaign, the PCs were all headed to or living in a city that was celebrating the marriage that just ended a 200 year long war. It was the biggest party the world had seen in eons, so everyone wanted to go, but for different reasons. The transport to the city was then attacked by interdimensional pirates...
Another campaign had PCs getting hired for caravan duties for money that was simply too good to pass up.
In a RIFTS campaign, everyone was in a small town for a variety of reasons (one was even in jail) when they all noticed a bunch of mysterious deaths...turns out the Mayor was a Vampire...AND was also one of the PC's uncles!
In a HERO game, the GM simply has a bunch of us superheroes answering the same alarm at a warehouse...and as newbies to the scene, none of us recognized each other as heroes. Result: big free-for-all in which the actual perpetrators got away...until the next adventure.
Yet another campaign started off with an adventure. The first player was in a tavern when a mysterious stranger entered. A fight broke out in the bar, and the 1st PC and the Stranger (PC2)fought back to back before escaping out to the back alley, where they encountered PC3 getting mugged. They helped the PC and then...well, lets just say each PC was introduced singularly and serially- each introduction required actions and choices. After a couple of hours, the players had had had a rollicking series of interesting encounters which established certain roles and interrelations.
And for the record, at any time, the players could have chosen differently, and someone would have been told "Roll up a new PC."