Responses like that are why women are often afraid or often intimidated to go to the gym. As a female you don't need to train any differently than males. I'm glad you realize that getting big isn't really a problem, as females have obviously low testosterone levels, and you don't just get big anyway without eating big. That's one myth that probably keeps most women in the cardio room instead of the weight room.
How long have you been training? If you are just starting out I'd just try and get your form correct, so that as you get stronger you will already have learned the techniques properly.
If you wish to get stronger you can vary the rep ranges you work in. I know lots of trainers will mindlessly assign a high rep program to females but never change it up. You can go much lower. Increase the weight and try reps of 3-6 for a few sets.
Getting strong isn't easy. Coming in week to week and doing similar weight in the same rep range won't help you get any stronger. Try to push yourself every time you go. Keep in mind that it takes a lot of hard work, and if you give it that extra effort it will definitely pay off.
So as I said, you can try to increase the weight you are using, and do less reps and this will help. Also, make sure you are eating enough as you'll require the added energy to lift intensely.
If you can, try to do some compound type movements. Presses, such as dumbell bench, or shoulder press are great, along with squats or lunges for the legs and glutes.
Rows are also great for the back, along with deadlifts or stiff legged deadlifts. You will get the most bang for your lifting buck by incorporating these into your routine.
Good luck.
Vegetables are what food eats.