How to connect with SQL Server database using .NET Core Class Library (.NET Standard)?

.NET Standard Class libraries don't work by directly referencing a DLL, because with .NET Core there is no guarantee the framework will be installed on the system and .NET Core applications can also run as self-contained applications which ship the framework libraries with the application and do not require a runtime to be installed before.

You have to use the NuGet package manager (or project.json or *.csproj in VS2017) to add dependencies. For SQLServer you need to add the System.Data.SqlClient package (link) if you want to directly communicate with the Database (i.e. w/o an ORM).