1. Add Unity to your project.

If you use NuGet you can use the Unity-package. Run Install-Package Unity in Package Manager Console. This will add the Unity library (and it's dependencies) to your project.

2. Create an implementation of IDependencyResolver.

For example:

public class UnityResolver : IDependencyResolver
{
    protected IUnityContainer Container;

    public UnityResolver(IUnityContainer container)
    {
        if (container == null)
        {
            throw new ArgumentNullException("container");
        }
        this.Container = container;
    }

    public object GetService(Type serviceType)
    {
        try
        {
            return Container.Resolve(serviceType);
        }
        catch (ResolutionFailedException)
        {
            return null;
        }
    }

    public IEnumerable<object> GetServices(Type serviceType)
    {
        try
        {
            return Container.ResolveAll(serviceType);
        }
        catch (ResolutionFailedException)
        {
            return new List<object>();
        }
    }

    public IDependencyScope BeginScope()
    {
        var child = Container.CreateChildContainer();
        return new UnityResolver(child);
    }

    public void Dispose()
    {
        Container.Dispose();
    }
}

3. Register your IDependencyResolver in your WebApiConfig.

public static class WebApiConfig
{
    public static void Register(HttpConfiguration config)
    {
        // Routes goes here..

        // Create your container.
        var container = new UnityContainer();

        // Do registrations here...

        // Assign your container.
        config.DependencyResolver = new UnityResolver(container);
    }
}