.NET Core templates are available in Visual Studio 2017. When installing VS2017, you have to pick the “.NET Core cross-platform development” workload. Once you do, you’ll have access to the templates:
- Click File – New Project.
- Expand Visual C# – .NET Core on the left side.
- Pick one of the templates.

If you’re on Visual Studio 2015, make sure you install Update 3 (or later) and the .NET Core SDK. Then the templates will show up in New Project:

It’s also possible to scaffold new applications on the command line, using either dotnet new (included with the .NET Core SDK), or yo aspnet:
# Create a new console app
dotnet new
# Create a new web (ASP.NET Core) application
dotnet new -t web
# Use generator-aspnet via yeoman
yo aspnet