I've found the best way to learn a new language is by doing, not just reading. And so, when I want (or need) to learn a new language, I generally do read a few chapters of a reference book on syntax, but then I dive right in and create something, rather than reading and reading book after book.
I've found that as problems and questions arise, answers are found (often on the internet). I also think this is why on the job training is so valuable, because you are producing a work product most of the time, even if it's a draft version - and so you are learning by doing.
I encourage people to just think of what interests them, and dive right into writing code or creating forms, etc.
Later on, after you have created project after project, a good reference book will teach you the fine details that at this point, you more easily grasp.
Also, the projects generally start out smaller and grow in complexity - from the simple "Hello World" app to a small and not very useful project, onwards to a full app. In terms of what aspects of the language I focus on, it depends on the applied use of the language - I never learn every API or framework to start (like with .NET for example). That would take far too long. I learn the core syntax, then branch out from there, researching each extension as needed. With a less modular language, like CSS or XSLT, I simply learn the most popular constructs first and add others as needed.