Last year I decided to learn the tools required to work as a data scientist. I was confident I already had the mathematical and analysis skills I needed, but I wasn't familiar with the tools of the trade.
Some googling brought me to Coursera, and the Data Science Specialisation run by Johns Hopkins University. It consists of 9 courses, and so far I've completed five. If you do the courses in order then prior knowledge isn't required, and I think the courses strike a good balance of brevity and depth.
The main downside to me is that the courses exclusively use R (which is popular in academia) and I would rather be using Python (which is more popular in Industry).
Each course lasts about 3 weeks and deals with a specific aspect of data science, such as statistical inference or machine learning. Key concepts and tools in each subject are explained and developed, and whilst it's not as thorough as a longer course would be, there is more than enough material packed into the lectures, quizzes, assignments and projects to apply to real applications.
I've read that the second half of the specialisation is a lot more technical than the first, so I'm looking forward to setting aside some time, working through the assignments and acquiring some useful skills!