Was your lovebird hand-raised and socialized before you brought her home?
I would definitely refrain from grabbing your new lovebird from the cage. That can be stressful and traumatic for the lovie. For now, reward her (him?) with praise and perhaps a favorite treat (a clump from a sprig of millet, a piece of a sunflower seed, etc.). One you get the lovie out of the cage, you can work on getting her to step up onto your hand OR a hand-held perch.
Here are some link to a series of articles that might be of interest:
Hand Taming Your Lovebird - Birds
The most important thing to remember is be patient. It can take quite a bit of time to tame and socialize any species of parrot.
If you haven’t done so already, you may wish to get your hands on a copy of Vera Appleyard’s book, The Lovebird Handbook. It’s a great resource for pet lovebird owners. She also has a pretty informative website: parrotparrot.com.
Best of luck!