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6Start with Gang of Four: http://www.amazon.com/Design-Patterns-Object-Oriented-Addison-Wesley-Professional/dp/0201633612/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1238418597&sr=8-1. A bit outdated but..
- learn about them (I personally like the C2 Wiki, others might suggest "Design Patterns" by the Gang of Four)
- apply them
- grossly mis-apply them (prime candidate: singelton)
- learn why number 3 was a mistake
- learn to apply them properly
That's more of a observation report than an instructional list ;-)
Though Code Complete is an excellent book (it is absolutely a must-have in my opinion), it is not the best of books to learn about patterns.
If you want to learn about patterns, a good book would be the Design Patterns book by the Gang of Four. It is a reference to some of the commonly used design patterns.
As for the patterns you mention: I see the MVC pattern more as an architectural pattern then a design pattern, since it effects the structure of the entire system (the architecture) rather than a more isolated piece of code. Singleton (not singletone) is an easy to grasp pattern, though it is overused and the downsides of it are often overlooked, so I wouldn't recommend to start with it (or at least, read it, learn the idea behind it, but don't just start applying it everywhere for the sake of using it - you usually don't really need it).
It's hard to recommend a pattern to start with, but I think Factory Method, Command, and Strategy are not too hard to learn, but I'm sure others could disagree.
"Head-First Design Patterns" may be a fun way to start (also check the discussion on the link).