Your last point, "I need some practical real-world problem solving approach on how to utilize these patterns'" is exactly what our .NET Design Pattern Framework is designed to do. Check it out.
As far as the GOF categories, I would not get hung up too much, this is just a grouping that has little bearing on how you choose a pattern. The best way to learn to apply patterns is by studying examples and then use these in your own work.
Hope this helps.
Jack Poorte, Apr 02, 2014