I can't provide specifics on an Adlib migration, but the following slide deck might help to give you an overview of the migration process to AtoM:
As noted in the slides, I would recommend using CSV exports to migrate over XML such as DC or EAD, if Adlib supports such an option or someone can write scripts to extract CSVs directly from Adlib's database. This gives you better mappings coming in (XML standards like EAD are highly flexible, so perfectly valid EAD exports from one system may not always map as expected on import into AtoM, but the CSV import is custom designed for AtoM), and there are also more tools for performing data cleanup prior to import (as the slides note, OpenRefine can be a powerful tool when used for data cleanup!).
If using CSVs for migration is an option, the following might help you prepare your description CSVs:
Additionally, some things to know about AtoM, that may also help the migration process: