Follow this process:
1.) What I have done is map a section of the AppSettings.json file to an object.
A.) Add the configuration settings to json file.
"MyConfiguration": {
  "DBServer": "MyDBServer",
  "DBName": "MyDatabase"
}
B.) Create a class to use strongly typed configurations.
public class MyConfiguration
{
     public string DBServer { get; set;}
     public string DBName { get; set;}
}
C.) Map the JSON configurations to the MyConfiguration object in the Startup class.   
public class Startup
{
   //Make sure you add this.
   public IConfigurationRoot Configuration { get; }
   public void ConfigureServices(IServiceCollection services)
   {
       ...
       var configSection = Configuration.GetSection("MyConfiguration");
       services.Configure<MyConfiguration>(configSection);
       //Use one of the following.            
       Services.AddScoped<MyClass>();
       Services.AddTransient<MyClass>();
       Services.AddSingleton<MyClass>();
       Services.AddInstance<MyClass>();
       ...
   }
}
See this link for an explanation of the differences between 
`AddSingleton()`
`AddScopped()`
`AddInstance()`
`AddTransient()`
2.) Change MyClass to have MyConfiguration object as a parameter of the MyClass constructor.
//add this using statement and corresponding package
//"Microsoft.Extensions.Options.ConfigurationExtensions": "1.1.1"
using Microsoft.Extensions.Options;
public class MyClass
{
    private MyConfiguration _configuration;
    public MyClass(IOptions<MyConfiguration> configuration)
    {
        _configuraiton = configuraiton.Value;
    }
}
3.) Add MyClass as a parameter of the AnotherClass constructor. Dependency Injection will create the MyClass or reuse it depending on the scope of the object and how you setup that up in the Startup.ConfifureServices() method.
public class AnotherClass
{
    private MyClass _myclass;
    public AnoherClass(MyClass myclass)
    {
        _myclass= myclass;
    }
    public SomeMethod()
    {
       //Use myClass here and you don't need to instantiate it.
       _myclass
       ....
    }
}