Most assets located in the DAM are used in AEM components. An author typically uses a component dialog - such as a PathFinder - shown here to select an asset.
This is a typical usage of Assets and use in AEM components.
Now when you want to use assets located in the AEM DAM in other websites - non AEM sites - you have to reference the full URL.
Assume that the server is named MyServer and you want to get content/dam/Sooners/soon.jpg -- therefore
MyServer:4503/content/dam/Sooners/soon.jpg
AEM does not have a tool that returns a list of URLs that corresponds to assets.
Using AEM APIS, you can develop a custom AEM service that would query the DAM for assets and build a list and return as JSON, or even get the list and put it into an excel spreadsheet. This is how i would think ppl that want URLS would solve this requirement.
Hope this helps...