I like learning the basics of new languages so I've done it quite a few 
times.

I usually take one or two hours to grasp the basic syntax of the 
language, then I implement a few classic algorithms and data structures 
(I start with Fibonacci, then I move on to things like quicksort, bloom 
filters, tries, state machines).

After that, I try to find a few (3-4) popular, reasonably sized Open 
Source projects in the language and I read their source code to get a 
grasp of what good code in this language feels like. I keep the 
reference manual at hand in case I don't understand something.

The next step is libraries: I check out how I can do common things such 
as network I/O, image manipulation, XML parsing, concurrency.

At this point I usually consider myself ready to do whatever I want with 
the language: start a new project, contribute to one, or completely stop 
using it.