One way to do it would be to create a Configuration Model based on your section/subsection from your appsettings.json file, add the configuration section in your Startup.cs class, then you can use the built-in dependency injection to inject the configuration anywhere you would need it.
For Example
appsettings.json :
{
  "MyConfiguration" : {
     "Configuration1" : "1",
   }
}
Your configuration model:
public class MyConfiguration 
{
   public int Configuration1 { get; set; }
}
Then in the StartupClass in the ConfigureServices method you have to add
services.Configure<MyConfiguration>(configuration.GetSection("MyConfiguration"));
services.AddOptions();
And when you want to use that Configuration somewhere in the code, you would just inject it in the constructor like so:
public class SomeClass 
{
  private MyConfiguration MyConfiguration { get; }
  public SomeClass(IOptions<MyConfiguration> myConfigurationOptions)
  {
    MyConfiguration = myConfigurationOptions.Value;
  }
//... more code
}
Then you can access it 
MyConfiguration.Configuration1