Personally, I would disagree with the advice to remove the pulley at one end of the torsion rod and slide the spring off that end. It's been years since I did my sister's garage door, but:
A) it seems to me that there must be something supporting the ends of the torsion rods where the pulleys are, and that "thing" may prevent the removal of the spring.
B) In my sister's case, she only had about a foot of space between the end of her torsion rod and the side wall of her garage. So, there really wasn't enough space to slide the new spring onto the rod easily.
C) My sister has a double garage, and her GDO uses two torsion springs. If I recall correctly, I was told that if one torsion spring breaks, it's best to replace both because the other won't be too far behind. And, if a person is going to be replacing both springs, it's not much extra work to hire a couple of teenagers to lift the whole assembly off the garage wall, replace both springs when the assembly is on the ground, and then put the whole assembly back up again.
It's been years since I did my sister's GDO, so I may be wrong on some points I'm making here.
Every web site you read about working with torsion spring GDO's will tell you it's dangerous, and that's mostly because of the possiblity of the winding bar slipping out of your grip and swinging around to smack you in the face or head. But, if someone has never done this kind of work, they don't know how much force will be in that winding bar, and therefore how dangerous what they're attempting to do is. And, that lack of certainty is fertile ground for the imagination to run wild with all kinds of tragic scenarios. When Y2K was upon is, because no one was certain there wouldn't be a problem, people were hunkered down in their own make shift bomb shelters with a month's supply of food and fresh water. Lack of certainty makes EVERY possible outcome a possibility.