I think it's intentionally left vague, to be campaign specific, and also to avoid having players point at the book and say "there, I meet the prereqs, give me my godhood." It's not something that should be achieved lightly or easily.
How it happens in my game? "Divine power" is a nebulous thing, and attainable by a very few means:
- Having it bestowed upon you by a god
- Taking it for yourself using some very, VERY hefty magic
On the former: You have to do something to really impress the hell out of that god, and make him/her want to have you around for all eternity. Game mechanic-wise, using the Divine Rank system in D&DG, I'd say a deity can give up his/her divine power (ie, points of Divine Rank) to mortal characters at will. Since this is so costly, most mortals who ascend this way start off at Divine Rank 0 (no cost to the deity).
On the latter: Of course, harnessing divine power isn't a simple task... Probably a Spellcraft DC 70 or 80 to even begin to understand the process, and magic well beyond anything the core books begin to describe would be required to carry it out. In other words, probably outside of the scope of what PCs can do, even into epic levels. That doesn't mean, however, that parts of the process can't be left behind (in the form of artifacts, locations, whatever) and used by your players (of course, these would be well-hidden and well-protected, either by their creators or deities who became aware of their existence.)
Keep in mind as well that the existing deities probably aren't going to be too happy about anyone attempting to ascend by their own hand. Still, you might get away with it, perhaps by having motives which don't conflict with any of the deities' (how Boccob became a deity, in my campaign: being so very true neutral), or managing to do so in total secrecy (as did Vecna, imc).
(BTW, Vecna is technically Undead in D&DG, not an outsider... He also resides on the Material Plane. Being an outsider is not a requisite for godhood, I'd assume, unless that's been errata'd like everything else

)