You need to manually edit the project file and add s to the default TargetFramework and basically change it to TargetFrameworks. Then you mention the Moniker with a ; separator.
Also you can put the Nuget package references in a conditional ItemGroup manually or using VS Nuget Package Manager.
Here is what your .csproj should look like:
<Project Sdk="Microsoft.NET.Sdk">
  <PropertyGroup>
    <TargetFrameworks>netstandard1.6;net452</TargetFrameworks>
  </PropertyGroup>
  <ItemGroup Condition="'$(TargetFramework)' == 'net452'">
    <PackageReference Include="Microsoft.Azure.DocumentDB">
      <Version>1.12.0</Version>
    </PackageReference>
  </ItemGroup>
  <ItemGroup Condition="'$(TargetFramework)' == 'netstandard1.6'">
    <PackageReference Include="Microsoft.Azure.DocumentDB.Core">
    <Version>1.1.0</Version>
    </PackageReference>
  </ItemGroup>
</Project>
Another workaround I do these days because of missing documentation is that I create a project in VS2015 and form the project.json using the available documentation and intellisense, then open the solution in VS2017 and use the built-in upgrade. I will then look at the csproj file to figure out how to make that configuration happen.
Multi-targeting more esoteric targets without a Moniker:
Microsoft:
PCLs are not recommended+
Although PCLs are supported, package authors should support
  netstandard instead. The .NET Platform Standard is an evolution of
  PCLs and represents binary portability across platforms using a single
  moniker that isn't tied to a static like like portable-a+b+c monikers.
If you want to target a Portable Profile it doesn't have a predefined moniker so Portable Profiles also can't infer TargetFrameworkIdentifier, TargetFrameworkVersion, and TargetFrameworkProfile. Also a compiler constant isn't defined automatically. Finally you have to add all assembly references none are provided by default.
This Example below is taken from a project that used the dynamic keyword so it additionally needed the Microsoft.CSharp assembly, thus you can see how it's references for different targets.
<Project Sdk="Microsoft.NET.Sdk">
  <PropertyGroup>
    <TargetFrameworks>netstandard1.5;net40;portable40-net45+sl5+win8+wp8</TargetFrameworks>
  </PropertyGroup>
  <PropertyGroup Condition="'$(TargetFramework)'=='portable40-net45+sl5+win8+wp8'">
    <TargetFrameworkIdentifier>.NETPortable</TargetFrameworkIdentifier>
    <TargetFrameworkVersion>v4.0</TargetFrameworkVersion>
    <TargetFrameworkProfile>Profile158</TargetFrameworkProfile>
    <DefineConstants>$(DefineConstants);PORTABLE158</DefineConstants>
  </PropertyGroup>
  <ItemGroup Condition="'$(TargetFramework)'=='netstandard1.5'">
    <PackageReference Include="Microsoft.CSharp" Version="4.3.0" />
    <PackageReference Include="System.ComponentModel" Version="4.3.0" />
  </ItemGroup>
  <ItemGroup Condition="'$(TargetFramework)'=='net40'">
    <Reference Include="Microsoft.CSharp" />
  </ItemGroup>
  <ItemGroup Condition="'$(TargetFramework)'=='portable40-net45+sl5+win8+wp8'">
    <Reference Include="Microsoft.CSharp" />
    <Reference Include="System" />
    <Reference Include="System.Core" />
    <Reference Include="System.Windows" />
  </ItemGroup>
</Project>