Sorry, but i just have to disagree with a couple of the previous reply's comments about Donne's attitude and lend a christian perspective on what he's really getting at.
Donne isn't afraid of death, but is very confident against death. As a Christian I can affirm his feeeling: we believe that Christ has rescued us from the threat of Death forever. I'd direct you to 1 Corinthians 15: 54-57, if you have access to a Bibile, because it's a passage Donne seems to have had in mind when writing. He personifies death so he can address and mock it directly. "Death be not proud" because (see 1 Corinthians) where is it's "sting"? It cannot hurt Donne anymore. He uses sarcasm in the 4th line "poore death" to emphasise death's cluelessness in this area and how pathetic it now is to Donne. Death doesn't even know what it's doing: it thinks it's killing people, but they "die not", and nor can Donne!
Donne is certainly not praising death at all at any place in the poem! But he is making it sound pleasant. When he says "From rest and sleep, which but thy pictures bee, much pleasure, then from from thee, much more must flow," Donne is simply saying, we get much pelasure from sleeping and resting, which are common images or 'pictures' of death. So, how much more pleasure should we get from the real thing, death itself! How much good men wish death would come more quickly ("and soonest our best men with thee doe goe") because heaven and eternal life will just be so awesome!
Donne brings death down further by saying in the sestet that death has no power, but is simply slave to "Fate, chance, Kings and desperate men" etc. (sorry, nothing more here as we haven't really studied it properly yet).
In the couplet, I would just say die, not extinct. It's an individual experience for Donne - I think. When he is in heaven, death is no more (because Christians belive in eternal life after the death). Death itself, in fact, shall die, but not men!
So Donne pretty much systematically detroys any might and dread death could have held, based entirely around his beliefs. Sorry if that was long-winded (i can get a bit excited about Donne) but i hope it was useful. What kind of sucks for people who aren't chirstians studying Donne is that there's heaps of concepts that they might not understand and have to work that much harder to get. But on the other hand, I think my issue willl be that I conenct so much with them, but will have to keep it purely academic!