Hi Cee-cee!
While I am not someone who is naturally skinny, working in a gym I see a lot of girls who are slim but unfit and lacking tone.
As Dee mentioned, you have some of the hard work already taken care of- you don't need to lose body fat, so you will be able to se the definition in your muscles pretty quickly.
Stick with weights and avoid a lot of cardio- you don't need to be burning a heap of calories. Make sure that you consume plenty of lean protein, especially after a work out and eat regular small meals.
Remember that as a women if you want to build muscle you will have to work hard. I'm a big believer in high weight with low reps to build muscle. You will sweat and it will hurt, but it will be worth it in the end.
Most women give up weights after the first session due to muscle pain post work out, but if you are sore the next day in the areas you have worked it means that you're on the way to stronger you!