In Visual Studio 2017 using the new .csproj format, the NuGet dependencies are automatically copied into the NuGet package based on the .csproj file's PackageReferences.
<Project Sdk="Microsoft.NET.Sdk">
  <PropertyGroup>
    <TargetFrameworks>netstandard1.3;net45</TargetFrameworks>
    <DefineConstants Condition=" '$(TargetFramework)' == 'netstandard1.3' ">$(DefineConstants);LIBLOG_PORTABLE</DefineConstants>
  </PropertyGroup>
  <ItemGroup Condition=" '$(TargetFramework)' == 'netstandard1.3' ">
    <!-- /* Package references for .NET Standard 1.3 */ -->
    <PackageReference Include="Microsoft.CSharp" Version="4.4.0" />
    <PackageReference Include="System.IO.MemoryMappedFiles" Version="4.3.0" />
    <PackageReference Include="System.Resources.ResourceManager" Version="4.3.0" />
    <PackageReference Include="System.Reflection.TypeExtensions" Version="4.4.0" />
    <PackageReference Include="System.Runtime" Version="4.3.0" />
    <PackageReference Include="System.Threading.Thread" Version="4.3.0" />
  </ItemGroup>
</Project>
So the only thing extra you need to do is add those dependencies from NuGet to your project. This can be done either by 
- Manually editing the project file (Right-click the project in Solution Explorer and choose Edit <projectName>.csproj)
- Installing the NuGet package via NuGet Package Manager
Changing Dependencies by Updating a .nupkg File
Alternatively, since a .nupkg file is just a .zip file with a different extension, you can change its contents:
- Unzip it with a standard zip utility to a temporary directory
- In the temporary directory, modify the contents of its .nuspecfile, adding additional dependencies as appropriate
- Zip the contents of the temporary directory again
- Rename the new .zipfile, giving it the extension.nupkg