How to configure Auto mapper in class library project?

You can place the configuration anywhere:

public class AutoMapperConfiguration
{
    public static void Configure()
    {
        Mapper.Initialize(x =>
            {
                x.AddProfile<MyMappings>();              
            });
    }
}

 public class MyMappings : Profile
{
    public override string ProfileName
    {
        get { return "MyMappings"; }
    }

    protected override void Configure()
    {
    ......
    }

But it has to be called by the application using the libraries at some point:

void Application_Start()
    {               
        AutoMapperConfiguration.Configure();
    }

So based on Bruno's answer here and John Skeet's post about singletons I came up with the following solution to have this run only once and be completely isolated in class library unlike the accepted answer which relies on the consumer of the library to configure the mappings in the parent project:

public static class Mapping
{
    private static readonly Lazy<IMapper> Lazy = new Lazy<IMapper>(() =>
    {
        var config = new MapperConfiguration(cfg => {
            // This line ensures that internal properties are also mapped over.
            cfg.ShouldMapProperty = p => p.GetMethod.IsPublic || p.GetMethod.IsAssembly;
            cfg.AddProfile<MappingProfile>();
        });
        var mapper = config.CreateMapper();
        return mapper;
    });

    public static IMapper Mapper => Lazy.Value;
}

public class MappingProfile : Profile
{
    public MappingProfile()
    {
        CreateMap<Source, Destination>();
        // Additional mappings here...
    }
}

Then in your code where you need to map one object to another you can just do:

var destination = Mapping.Mapper.Map<Destination>(yourSourceInstance);

NOTE: This code is based on AutoMapper 6.2 and it might require some tweaking for older versions of AutoMapper.