When we've connected to third-party CMS systems, we've used Dynamic Media for asset delivery (presuming you need imagery, videos, 3D files, and/or PDFs--for other file types, you'd have to use a publish instance for delivery).
Vignette should be able to leverage imagery and other supported assets via a Dynamic Media URL with a bit of customization on that side.
In order to determine which assets are needed by Vignette, it depends on how automated the content creation process is within that CMS. If you have authors putting together custom pages, then you can use the Asset Selector to access the DAM and choose relevant assets for Vignette. If you have somewhat automated PDP and category page assembly (similar to a eCommerce paradigm), then you'd want to query the DAM for relevant assets by SKU with a custom endpoint.
This is just high-level architecture. Lot of work to make any DAM-to-CMS integration work well, but hopefully these tools Adobe provides are good starting points for the dev work.