Creating Dependency Injection with ASP.NET Core is fairly easy. The documentation explains it very well here and this guy has a killer video to explain it.
However,
I recommend you use Autofac, there are anothers fwk like unity, ninject, the benchmarks autofac has excelent perfomance.
http://www.palmmedia.de/blog/2011/8/30/ioc-container-benchmark-performance-comparison
Here is the integration with MVC (and works with all class)
http://docs.autofac.org/en/latest/integration/mvc.html