How do i get rid of the dirt build up on the plastic lip on the iPhone 4 white?

I have a black one, but I use a new, dry toothbrush to clean the grit off. If you need to, use a TINY amount of rubbing alchohol on the brush.

Here are Apple Steps:

To clean iPhone, unplug all cables and turn off iPhone (press and hold the Sleep/Wake button, and then slide the onscreen slider). Use a soft, slightly damp, lint-free cloth. Avoid getting moisture in openings. Don’t use window cleaners, household cleaners, aerosol sprays, solvents, alcohol, ammonia, or abrasives to clean iPhone. The front and back glass surfaces have an oleophobic coating. To remove fingerprints, simply wipe these surfaces with a soft, lint-free cloth. The ability of this coating to repel oil will diminish over time with normal usage, and rubbing the screen with an abrasive material will further diminish its effect and may scratch the glass.

There is an App for that: http://www.apple.com/webapps/entertainment/lickmyphone.html

Until your iPhone is OFF of Warranty be careful cleaning it. Once OFF Warranty, you could try basic cleaning techniques at your own risk.