You mention both design patterns and coupling. These are separate concepts so I'll deal with them separately. The only real connection is that design patterns tend to promote loose coupling (since it's a major aspect of good design).
The concept of Design Patterns is actually quite simple: They're just a set of templates of how to deal various common problems. There are 2 main reasons that they are popular:
- They are 'proven': they have been used before many times and the benefits/drawbacks of each are generally known, in particular any subtle issues that might cause big problems are known.
- They provide a common set of terminology, and so enable easier communication. If someone says "class X plays the role of the observer in the observer pattern" then developers who are familiar with the pattern can immediately grasp what's going on.
How do you know that you've implemented it correctly? That's a tricky one. For most patterns it's simple - you've either grokked it or you haven't. Some patterns are less clearly-defined than others - e.g. model-view-controller. Patterns like that are better used as general guidelines. The specifics of how you implement it are less important than understanding the reasons that the pattern exists and what it's meant to accomplish.
Design patterns aren't 'the one true way'. Often you'll either need to adapt them for your specific purposes, or sometimes there just won't be any patterns which fit the requirements. Forcing a design pattern where it doesn't fit is a bad idea; it's like using a really good hammer when what you actually want is a screwdriver.
This is a really important idea in computer science. Since requirements for most software projects change over time (sometimes significantly) then the ability for a design to cope with changes is important. Coupling is basically the measure of "how hard would it be to swap out this component for another one?" The 'component' could be a method, class, package, library, etc.
There are various types of coupling listed in this Wikipedia article.