Take pictures on Nikon D3000 without using viewfinder?

I recently purchased a Nikon D3000 and I was wondering if there was a way to take pictures without using the viewfinder and using the screen instead.

No, there's not. That camera does not support "live view", as the feature is called.

Serious photographers don't use live view…

Supporting a heavy camera such as a DSLR at arm's length will certainly result in camera shake.

With the viewfinder, you can get the camera up tight close with your elbows tight against your body, and you will have better photos as the camera will not wobble as much. This is a better method than trying to use the screen.