In the original FF, Doom was a college... well, friend is not the right word, but acquaintance of Reed Richards. Both were, of course, geniuses. Doom was making some sort of invention to travel to other dimensions (I think it had to do with getting his mother out of some demon's claws), and Richards saw the plans and pointed out some error that Doom, of course, ignored. Doom built the machine, tried to use it, and had it blow up in his face, giving him a noticable scar.
Doom then left and sought out some weirdo monks - I think in Tibet. He learned mystic stuff from them, and forged his armor. Being the impatient man he is, he refused to wait for the mask to cool down, putting it on while it was still red-hot, thus turning his scarred-but-still-OK face into a burned mess.
In the Ultimateverse, Victor van Damme (which was a name his family used to hide the implications of the von Doom name - the family apparently has ties to ol' Vlad the Impaler) was a kid genius just like Reed Richards and Susan Storm (well, late-teens anyway). They were working in a big government project on some sort of dimension-piercing apparatus. Van Damme had made some changes to the apparatus without Reed knowing about it, so when the machine was activated, Reed, Sue, van Damme, Reed's buddy Ben Grimm, and Sue's brother Johnny (and maybe one more person - see below) disappeared and were scattered across various places. In the process, they got weirdified - Ben Grimm turned into some sort of stony Thing, Johnny Storm got the ability to turn to flame, Sue Storm could turn invisible, and Reed Richards' body got a weird lack of fixed shape - classic elemental associations: Ben - Earth, Johnny - Fire, Susan - Air, and Reed - Water. Then we learn that van Damme has apparently turned into some sort of metallic monstrosity, and see hints that someone also turned into the Man-Thing. These two would then be Metal and Nature.
Ultimate Four #7 which showed Doom's background used to be online as a preview somewhere - ah, at
http://www.milehighcomics.com/firstlook/marvel/ultff/
Here are some of the relevant picture for the above story:
The people getting transferred, including Man-Thing:
http://www.milehighcomics.com/firstlook/marvel/ultff/page04.html
First full picture of Doom:
http://www.milehighcomics.com/firstlook/marvel/ultff/page22.html
Flashback to Victor van Damme being told by his father about his heritage:
http://www.milehighcomics.com/firstlook/marvel/ultff/page07.html