I know how to create custom ASPX pages and a deployment package, but I need to implement a custom ASPX page in SharePoint 2010 which uses its own custom database.
Please advise me how to do this.
the best way to do this is to configure BCS (Business Connectivity Service) to fetch data from external database to SharePoint and than work on the lists and libraries SharePoint.
Here are some articles to read:
Hope it helps,