Nikon lenses and the DX format?

I'm very confused with the focal lengths of Nikon DX format cameras. I own a Nikon D5000. When I shoot with DX lenses on my camera, do I still need to multiply 1.5 because of the crop factor to get the actual focal length? Or the focal length is as it is? I super need help!

The focal length remains the same, it's just that because the sensor is smaller you get a crop factor. That crop factor comes around because light that would hit a larger sensor falls outside the area of a smaller sensor.

This only really becomes clear when you get to extreme focal lengths. When you use a very wide angle lens you'll find that the depth represented in your images becomes compressed. If you use a lens with the same focal length on an FX (full frame) and DX (smaller/APS-C frame) you'll see that the depth compression is identical, it just that part of the image has fallen outside the area of the sensor on the smaller sensored camera.

Your 50mm lens is always 50mm. But the sensor is a bit smaller than the usual FX, so it gets cropped - 1.5x.

Here's a DX and FX Explained - http://www.the-dslr-photographer.com/2011/09/nikon-dx-and-fx-sensors-explained/

Screw crop factor. Focal length does not change with sensor size. Only angle of view does. You shoot what you see through the viewfinder and if required by law to record the aperture size, list down exactly what you used (what's indicated in the EXIF data). No conversion, no equivalents. Just as it is.

Yes, the crop factor still comes into play with dx lenses. The link below talks about how it works. Basically, the dx lens is just smaller because it doesn't need to be as large due to the smaller sensor. The focal length, say 50mm, will be the same no matter which camera type it's on. The dx sensor will use a smaller portion of the lens giving you a narrow field of view creating a crop effect. You don't gain any focal length, just lose some of the photo that would be captured on an fx sensor.