Pick a room you can close off for the new girl, complete with some place to sleep, food/water dishes and new litterbox & litter. Visit frequently but keep your resident cat out for now. They will investigate each other through/under the door, become accustomed to the other's scent (a cat's world is mostly scents,) and new kitty gets familiar with the rhythm/noises of the house. There will probably be some growling and hissing through the door but that's normal and will subside as each grows accustomed to the other's scent. If new kitty immediately hides in the safe room (i.e., under furniture,) just continue this routine until new kitty comes out to you when you're in there (without resident kitty.) Pet her, maybe play with her using a wand or some other cat toy. If she's outgoing and never hides, all the better!
After she has started coming to you for affection or playtime when you're in the room for a couple of days, you can leave the door cracked a little but only under supervision. See how they react. Try to keep your resident cat out of the new kitty's room for now. Remember, the new kitty considers this her "safe place" where she is never in jeopardy. What you're looking for is the absence of severe hostility. Nose boops, smelling each other, growling, hissing, the occasional whap at one another, charging each other is normal. If one cat is cowering or attacking or it looks too aggressive, separate the cats and close the door, leaving new kitty in her safe room. Cats have a natural way of establishing their social order.
Just keep doing the cracked door thing every day or two and see how it goes. You will see that it will eventually turn into more playtime and less growlies. The new kitty will venture out of her safe room to explore (leave the door to the safe room open.) The resident cat will shadow her, smelling her, maybe a perfunctory whap, etc. If the new kitty gets spooked, she will instinctively run back to her safe room because, well, it's safe! If she does that, just close the door to keep resident cat out and try again the next day.
Before you know it, they will be a happy couple. The obstacle here is that cats abhor "change" so, after a while, the new kitty will no longer be considered a "change." It will be obvious to you when the transition is over you can regain possession of the safe room for your use. Put the new kitty's litter box next to the one you have for resident kitty.
My experience doing this is that the period of transition can be as little as one day or as long as about a week. From your description, I think your new kitty will become a comfortable member of your clowder very quickly.
Good luck, congratulations, and keep us posted!
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