Yesterday I outlined a strategy of rapid learning: the core is doing many problems with feedback. When you need supplemental information, you can do either a quick lookup or refer to lectures or a book. I can't tell you how the strategy worked for me just yet! My interview was rescheduled.
How can you apply this strategy to your own learning? The problem is, well, you need problems. Preferably lots of them, well sequenced, with feedback. Books are the best bet, but there is an emerging class of web apps providing problems and feedback. I've bolded the ones that let you do everything in the browser, including verification of your answers.
Code.org has good coverage of interactive beginner tools. To quickly learn a new language, Code School and Codecademy cover a variety and here are some options for Ruby (or here), Python, Java, Lisp, Prolog, OCaml, Clojure, ClojureScript. Not web-based but here's a list of repositories for koans in many languages, and a mixed variety of resources. For practice with algorithms and other such challenges, use Project Euler (more math-oriented) or HackerRank (topics from algorithms to AI and data). Kaggle is specifically for machine learning and ranges from simple data sets to paid competitions, where even professionals can hone skills. For more introductory data tools, there's DataCamp.
Khan Academy (which seems to have gotten harder to navigate) covers most of K-12 math with problems and videos. For competition math (similar to what shows up in quant trading interviews), I grew up on Art of Problem Solving, but Brilliant is a new site with an excellent experience for doing problems. I haven't seen anything in more advanced math other than my own project Rudinium for real analysis.
DuoLingo currently covers Spanish, French, Italian, German, and Portuguese, and is excellent in both web and mobile forms. I wouldn't say it's the best method at an intermediate level or beyond, but to get started quickly and have fun, it can't be beat. Skritter covers Chinese and Japanese with handwriting recognition for characters.
I seem to come across something to add to this list nearly once a week--and I'm not even covering mobile apps. Obviously I think it's a model that should be repeated broadly. There isn't a whole lot of complexity to the domain-general part--most LMS or course building software would be overkill. Oppia is one web tool specifically for interactive learning, but it'd be awesome to have one with features like analytics and spaced repetition built in. Of course there are SRS tools already like Anki or Cerego, but these tend to be limited to simple flashcard-type questions.
Let me know what I missed!