When you lay her down, try leaning over the crib and rubbing her forehead and down her temple, or rubbing her hair. Something to keep soothing her after you lay her down ya know? Then once she's asleep, stop. We did this with LO and it clicked with him around 3 weeks. Now we can lay him down laughing and giggling and he'll be asleep in 5 minutes.
Are you swaddling? Make sure your swaddle is nice and tight and that will probably help to. We don't swaddle anymore, but that helped a lot when it came to that early stage.