Monique, I'm so sorry to hear about your friend.
But what a wonderful thing you're doing.
Keep her in a separate room for as long as it takes. Get a t-shirt, rub her all over with it, and put it under your other kitties food dish. Rub your other kitties with a t-shirt, and put it under her food dish. This will help them associate each others' scent with "good" things.
I'd consider getting some feliway spray - it'll help de-stress everyone. You may want to consider some Bach's Rescue Remedy for her transition (dab it behind her ears and put it in her water dish). You can probably find it cheaper somewhere else, but it is available here: http://www.catfaeries.com
Let them get used to the scent and sound of each other - and give her a little while to get used to her new room and new family. When she's made the room "her" territory, then you can let them sniff each other through the door, or bring them in one at a time for 15 minutes of supervised attention or something.
Another thing you can do is get a couple of new catnip toys. Give one to her and let her drool all over it. Let one or several of your other cats drool all over the other one. Then pick them up. A week later, give her the one some of your kitties drooled on, and give your kitties the one she drooled on.
Praise the kitties for not hissing at the door or for any not negative interaction. Maybe keep some new toys handy for when you start making the intros - help your gang to think it's a total party having the new kitty around.
And give your current kitties lots of love and attention. I don't know if your other three are girls or boys, but our boys are always very good with new intros and it isn't a problem - but the girls always take a lot of time to adjust. Spooky takes 6 months before she'll stop swatting and hissing at newbies - but she doesn't go out of her way to attack them or anything. But trust me - even if there's hissing and swatting at first, even if Callie's in her own room with a slow intro, it may happen. Just let them work it out as long as no one looks to get hurt.