I brought home a new cat today, and I have a few questions!

Okay well I adopted a gorgeous tabby/torti from the local animal shelter today. She is 3 years old and had been at the shelter for 10 months! We bonded immediately and I knew I had to give her a home. Her name is Saffy

Anyway, the poor thing is terrified! I've heard this is normal (never had cats before) and that she needs to adjust to her new home, and will be scared for a while. I've put out food in the laundry but shes too afraid to roam around the house. I'm worried she's hungry/needs to go to the toilet and cant cause shes too terrified! What can I do?

Also she wont let me pick her up, but she did at the shelter.. but I assume thats also just because shes scared and needs to adjust. Would I be right? And, her tail keeps shaking a little violently, I also assume for the same reasons but I've never seen a cat do it before? It may seem like silly questions to ask but shes my first cat and I want her time at her new home to be perfect
Thanks in advance!

Not silly questions at all!!!
I would start by giving her a "safe" room. Keep her confined in there, just for now, sounds mean but its not. Put all her stuff in there, food, litter, toys. Make sure she has spots she can hide though. She needs to feel safe. Keeping her in a smaller space right now is better, the whole house may just seem TOO much to adjust to after the shelter. Spend lots of time in the room with her, just going about your business. Be on the laptop, do crafts, read (aloud) to her. THis sounds silly, but act cat like if she is watching you. Yawn, stretch like a cat, Lay on the floor on her level and close your eyes, while "looking" in her direction. Get back up (to sitting, not standing) and blink really slow. Its cat talk for, well, Im stretching and sleepy, lol Shows them you mean no harm.
Hold off on trying to pick her up for now, let her get to trust you more first.
Cat nip and treats, always good, get a jar to keep her treats in, set it next to you while you sit on the floor, she will soon hear you and the jar mean tasty snacks. ( you can also take funny pics of her as she sticks her head into the jar when she thinks you are not looking!
You will do fine, patience is the key.

Hi, lots of good advice. Just remember that cats relate to territory first, us second, and when they're comfortable in their places, then they'll respond to us better. I'm curious - is the cat spayed? The tail shaking is a bit of a signal that she might be marking her space and you don't want a lot of that, though males are much worse about it. If she's not fixed, it would be a good idea to schedule it as soon as possible, plus it's much better for her health (when she gets older) if it's done now. Also, I wouldn't let her out at all (if you had any plans to do so, though I think not doing it ever if best) until she's been with you for quite a while and definitely sees your house as 'home'. I personally would take advantage of her readjusting to being there to keep her in for good, but maybe leash training her or thinking about an enclosure (see the type of thing available in the big ad at the top of this page, or Google more).

Thanks you two for the help, I might just take up that suggestion of keeping her in one room. We've had her for just over 24 hours now, and she's eating dry food if I put it in front of her but she wont drink or eat wet food. She hasnt been to the toilet in her whole stay here either :S
To Larke: Yes, she has been fixed. She's shaking her tail a lot!