There are a couple strategies you could take. Inheritance is the most obvious one. You might also consider composition. Can you give us some more details about what the object is and what properties you need to add to it and why?
After seeing the expanded question:
Either strategy outlined above (composition or inheritance) will probably work for you. Personally, I prefer composition. I think it better insulates you from changes that might be made to the third party library. It also forces you to work through the public interface of the library class, which is preferable when you have no knowledge or control of the internals of a class.
Here is the most basic example of composition.
public CompositeClass
{
private ResultClass _resultClass = new ResultClass();
public IList<Item> Results
{
get { return _resultClass.Results; }
set { _resultClass.Results = value; }
}
public int TotalResults
{
get { return _resultClass.TotalResults; }
set { _resultClass.TotalResults = value; }
}
//
// New Property
//
public string Description { get; set; }
}