@PGWP1
https://www.dubaipolice.gov.ae/wps/portal/home/services/individualservicescontent/goodconductcertificatecatalog
The online form is linked above, you need to select "outside UAE" for your location and "No" when asked if you have Emirates ID.
To download the fingerprint card, there's a link in the online form under "Biometric Card Photocopy". Although it says you need to pay via GCC-issued cards, there are people here that managed to pay using other credit cards. In my case, I was able to even use a debit card (Philippines).
Now the fingerprints, there's 3 things you need to do:
1) Make sure your fingerprints are taken by an authorized person.
2) After 1, it needs to be authenticated by your country's Foreign Affairs department.
3) After 2, it needs to be authenticated by the UAE Embassy in your country.
Please note that the fingerprinting process may slightly differ depending on which country you're coming from---Some countries have the police do the fingerprints, some countries have services where they will do steps 2&3 for you altogether, and some have all-in-one services, etc. But no matter how it's done, those 3 things listed are what Dubai Police's going to look for on your fingerprint card.
When all things are settled**, you need to send your authenticated fingerprints, 2 nos. of passport-sized pics, your payment receipt (for good measure), passport photocopy and previous UAE residence visa passport page photocopy to:
Criminal Investigation Department
Good Conduct Certificate Section
Dubai Police Headquarters
P.O. Box 1493, Dubai, UAE
** I placed all of these in one envelope/folder, and marked clearly on the outside 'To: CID Good Conduct Certificate Section', 'Re: Police Clearance Certificate Application' and lastly my reference no. As I don't frequent the forums, I hope the others with the same case can refer to this. Happy new year everyone!