I'm a bit confused by your questions, so I'm not sure if this will help:
The only "official licensing process" is the contract you create and sign together with your client.
One resource for licensing language is the GAG Handbook (Graphic Artists Guild Handbook of Pricing and Ethical Guidelines).
There is nowhere you need to file your contract - just make sure you keep a copy.
If, by "file a license" you actually meant "register for copyright" then you can find out detailed info. about that at the US Copyright Office website: http://www.copyright.gov/
If your client will be owning the copyright to your illustrations, then it is they who will register for the copyright (if they choose to - it's not required).
If you license to your client use of your illustrations for their project, and you retain all other rights, then it is you who would register the copyrights (if you choose to).
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