I would not seperate guzmania pups at all. Guzmanias are one of the hardest bromeliads to get to root and they will probably die. Keep the pups on the mother plant and they will be much healthier and grow faster.

So what do I do about all of the dying leaves from the mother plant that look so horrible right now? They are all browning and starting to dry out.

If the plant bloomed then it is normal for the leaves to die off. Just remove each leaf as it becomes dead.

To separate the a pup from the mother plant, gently remove the mother from the pot. Then, using a sharp knife cut between the mother and pub. You can even angle the knife a little into the mother to make sure you get all of the pup. Plant the separated pup in a smaller container and put the mother back in her original pot and fill in with potting medium.
If you ask a dozen people what potting mix to use, you will probably get twelve different answers. What everyone seems to agree on is that it should have good drainage. Some good potting mixtures are equal parts of peat, bark and perlite or equal parts of peat, bark and sand. A cactus mix could also be used.
Yes, you should keep the mother plant alive because it probably will produce more pups.

I strongly advise you not to detach the pups. Offsets of this genus can be very difficult to root. If you leave them attached, they already will have access to a set of roots and will be much more likely to prosper.

Uh oh...I just separated a bunch of pups. I haven't had much experience with guzmanias, so can anyone tell me the best way to insure they'll live? I have them in half peat/half perlite and I dipped them in rooting hormone.

I managed to keep a separated Guzmania pup alive (although now i never separate pups from any bromeliad unless i am giving it away or something). I potted it up in a fast draining mix (no rooting hormone), put it under a chair on my balcony so it wouldn't get too much sun, and tried to keep up with it's watering. I think the humidity outside saved it more than anything i directly did. It's now moved up to get a little more light and is blushing a nice red in the center, i think it might be considering a bloom! Next time i'm leaving the pups on though! :)

Thanks for all of the info. I am going to keep the pups where they are as I do not want to have to fight to try and keep them alive. They look really healthy right now and I would like to keep it that way.

Cheers,
Sean

The Central Coast NSW Bromeliad Society, Has articles on pup removal and general Bromeliad growing information, lots of bromeliad garden photos.

Here is a link that might be useful: The Central Coast NSW Bromeliad Society

Gee, I've never had any problem removing or rooting Guzmania pups, provided they're mature enough to be removed. Of course, I've got a warm, humid environment, so that may be the problem for the rest of you, although I wouldn't think the Florida people would have a problem. I usually let them get a little bigger than I would, say, an Aechmea pup, but most of them have about a half-inch or so of stolon at the base, so removing them is not the delicate operation that it is on some of the big Vrieseas. The one exception to this is Guz. sanguinea. You've gotta be a brain surgeon to get those off!