New puppy has roundworm and fleas...

I would take it to the vet and do what the vet suggests.....ASAP....

Pretty much ALL puppies have roundworms.  They're carried by the mother ans passed to the baby -- but literally they are carried by the mother since SHE was a puppy and she got them from HER mom... etc.  They're just a dog thing and aren't zoonotic (transmittable to people). 
 
however, that being said -- all puppies have to be wormed, but a good breeder SHOULD have wormed them already.  So .... altho yeah, all pups have roundworms, you shouldn't see a ton of them from a good breeder, and a good breeder shouldn't be letting puppies go that young without thorough worming and vetting either.
 
But no, the pup shouldn't have had fleas -- a good breeder would have had Frontline on Mom and the baby would have been bathed before placing. 
 
Talk to your vet -- I wouldn't use Revolution (it doesn't kill fleas unless they bite anyway), but you will also want to spray your carpets the same time you take the dog to the vet - something with a good egg inhibitor.  I haven't read the label in a while but your vet will tell you what is safe for a pup of that age.
 
You can bathe the pup in pretty much ANY soap and it will stun fleas.  Then pick them off and put the stunned flea in a dish of soap (yep, just Dawn or anything) -- and flush that down the toilet.  Human dandruff shampoo (like Head and Shoulders) tends to work particularly well to stun fleas so you can get rid of them. 
 
Much depends on how old the pup is.  If you haven't had the pup to a vet yet, then it needs to go anyway.  Have a fecal done (take in fresh poop if possible -- snag it in a baggie and put in the fridge before you go -- bacteria will grow in moments so it needs to be refrigerated -- sorry, that's gross but true).  A brought in sample is better than them getting a sample with a rod, but if you can't accomplish it, they can get one from the dog without trauma.  But having a fecal done is a GOOD thing -- it will tell you if there are other parasites that can't be eradicated with simple wormer.

Pretty much ALL puppies have roundworms. They're carried by the mother ans passed to the baby -- but literally they are carried by the mother since SHE was a puppy and she got them from HER mom... etc. They're just a dog thing and aren't zoonotic (transmittable to people).

 
Why is this?  If my puppy who has no worms,,,because she was treated for them,,,goes on to have her own litter,  why will her pups get worms???

I mean, my puppy sleeps on my pillow above my head and this just FREAKS me out!! 

I suspect getting the fleas out of the house will be difficult.  Oh well...  

There's a long huge veterinary explanation for this but the Callie-ese explanation is that roundworms will lay larvae in muscle tissue -- so they lie dormant the entire life of the pup/dog and only are triggered to come out by something hormonal during pregnancy. 
 
This was news to me as well -- they say rarely but occasionally a dog may escape but typically virtually ALL puppies have roundworms. 
 
As long as you get rid of them while they are still in the intestines it's relatively easy, but some are let go and you'll see pups vomit them as well.  Pups can die from an infestation of round worms this bad. 
 
Apparently they've never been able to figure out how to kill the larval stage of them -- so by the time they are in the muscle tissue they can't kill them.
 
But roundworms aren't zoonotic -- they ARE just a dog thing - so it's no danger to the humans at all.  Just very very gross.
 
But it's like I said -- a good and careful breeder would have wormed the dog before you got it.  A good and careful breeder, I suspect, wouldn't let a dog GO until it was old enough that they were satisfied that they'd elminated the roundworms and the pup was old enough to be satisfactorily vaccinated with first vacs (like around 10-12 weeks).  A really good breeder isn't going to bow to the "OH can't I take him NOW?? He's SOOOOO CUTE!" thing -- A really good breeder is gonna tell you "no way!!!  This pup stays with ME until I know it's healthy enough and old enough to have the best start I can give him!!"
 
So that's where you get into the 'good breeder' part of it -- make sense??