1. Learn GoF design patterns. Be amazed by the cleverness.
2. While learning others languages, discover that other approaches remove the need for GoF design patterns at all.
Example: Visitor isn't needed in a language with double dispatch (like Lisp). Chain-of-Responsibility is just foldl. Factory for dependency injection is just a closure or a partial function. And so on.
If you are in luck, a language gives you first class support for abstracting new patterns. (Eg in assembly a procedure is just a pattern and convention, most modern languages help you by providing procedures. Same languages are very good at being extended. Lisp is a good example, and so is Haskell. Even Python is great in that respect compared to, say, Pascal.)
I am still trying to figure out what dependency injection really is. It's seems like only the Java guys have a need for it, but they rave about it.
foo() { service = someRemoteService(authn, authz); http://lookingglass.internal.adm.bol.com/?page=TAM+Middlewar... }
is replaced by
foo(service) { do_something_with_service(service) }
It makes replacing service with fake_service_object easier, thus simplifying the test process.
Common use case: If your service was a remote database, you can replace the database handle with a mock object which pretends to be a DB but is actually a simple object returning hardcoded values.
But most devs don't want to be in those positions :) Cause it involves a bit more people wrangling than code wrangling.