As others have said, it depends on so many factors. I'm still learning perl (my primary language) ten years after I started. I was writing working code in Ruby after a weekend, and I believe I could be fluent in it within a week or two of working primarily in that language. Python I've never set out to learn, but several years of working with Python projects and developers has given me the ability to patch in what I need in existing projects without a struggle (but I couldn't start from scratch).

It also depends on how you learn it, and who you learn it from. The pickax book is a fantastic book for learning ruby. Same goes for Learning Perl for perl. I've never seen a similar book for Python, but one might exist? For JavaScript you cannot beat Douglas Crockford's videos at the Yahoo! Developer Network. Absolutely fantastic...taught me everything I needed to know to be productive in the language in one weekend. JavaScript also happens to be a great learning language, as it has both functional and imperative constructs and pretty simple syntax and minimal keywords.

Find all of them (along with a few other good ones--Joe Hewitt's Firebug demo, in particular, is what you'll want after the Crockford vids) here:

http://developer.yahoo.com/yui/theater/