How can I get my girl to be more active in the bed?
I could take this a lot of different ways. Is your girlfriend simply holding still while you fuck her, then falling asleep as soon as you come? Does she do what you ask her to do, but never ask you to perform any specific act or technique for her? Is it your job to always initiate sex? Do you feel unsure about whether she's ever had an orgasm, or are things good in that department but you want more variety? Are you curious about her sexual fantasies? Or is she refusing to have sex with you most of the time?
When looking for a solution to a relationship problem with sex, it's helpful to be as specific as possible. You might want to get a notebook and write down your perceptions of how the sex is now and how you want it to be different. Keep this private so you can be as negative about the problem as you need to be. Vent some of your doubt or anger, perhaps. Then you can also be as wild about the solution as you'd like. Why not describe exactly what your ideal sex life would look like? There's no point in trying for anything else. Be honest about what's happening and not happening.
If she isn't responding to your sexual technique, you probably need more information about how her body works. The best way to find out how your partner comes is to watch him or her masturbate. If your partner would be too embarrassed or would find that word upsetting, ask her to "touch herself" for a few minutes so you can see where she puts her fingers and how hard she presses down. Most women like clitoral stimulation. This is how they get turned on, and they need it to continue during intercourse if they are going to come. Learning how to go down on her (gently! gently! and shave first!) could have her wiggling around like a porn star.
Create a safe space in your bedroom for sharing sexual fantasies. Ask her to talk to you about what she thinks about when she masturbates. Some women have graphic X-rated stories they tell themselves; others may not. For some women, desire only happens when they feel romantically involved with their partner. They need flowers, compliments about how they look, somebody who listens when they've had a hard day, maybe somebody who does a chore around the house to save them some work, or someone who puts on some music and lights some candles in the bedroom.
If your girlfriend had a traditional upbringing, the idea of initiating sex may be quite new to her. She may feel very shy or reluctant to do this. Sex might be easier for her if she can see it as something you need that she can take care of. She may be so out of touch with her own sexual needs that she doesn't know when she's horny. Here's a secret guy hint: Keep track of her menstrual cycle. Get a little one-page calendar and mark it, then put it in your wallet. Note if she gets amorous in the middle of her cycle, when she is ovulating, or right before, during, or after her period. Then cooperate with Mother Nature, you dog. Another secret guy hint: When she is almost ready to bleed, be sure to provide a heating pad, Advil, and chocolate. Massage her tummy and feet and tell her you're sorry she doesn't feel well. She will never leave you if you do these things.
Here's an idea that doesn't require her to say out loud when she wants sex or what she wants to do. Take some index cards and cut them in half. Each of you should take, say, ten of them. Write ten sexual things you would like on these cards, then throw them into a jar. Next time you have the time and space for lovemaking, take turns drawing a card. The evening has to include at least 15 minutes or perhaps half an hour of whatever is on them.
Other ways to spark her imagination are to visit a sex toy shop, look at websites with erotic material, read each other some erotica, rent an X-rated movie and watch it together, take a massage class together, or take some classes on other topics. I hope at least some of the ideas in this answer were helpful. If not, please write again with more details.