The Abu Dhabi Police Clearance is also known as the Good Conduct Certificate.
I have no direct affiliation with the Abu Dhabi Police but this is the process I followed on February 2012 when I needed a Police Clearance for employment:
1. Purchase an E-Dirham card from any NBAD branches. AED 60.00 for Police Clearance application or ask how much the fee is, in case the price changed.
UPDATE: Debit card and credit card are acceptable.
2. Get a Letter of Request provided by the company asking for the police clearance. This is in Arabic.
3. Attach your UAE ID Card. Passport with visa, ID photos and fingerprints are not needed.
4. Go to the Police Station in Salam St. They close at 1:00 PM. Personal appearance is not needed. A proxy can go for you.
UPDATE: Alternative is Al Shabeeya Police Station in Najda – Timing 7:30 AM -12 noon.
5. Your Police Clearance will be delivered to you after one week, or you can pick it up at the post office when you receive the Empost text message.
Your Emirates ID card makes everything easier.
To know more, go to the AD Police website here.