I have trained a class of people who paid hundreds of thousands of Naira to learn data analysis with R and I have equally paid a lot in books and online training to horn my R skills. For Python, I haven't yet trained a class on it but I have paid a lot too on books and courses to learn it.
Hands down, the best training resource is hands-on projects. After that, training classes and books rule. And today I will be sharing with you the best free training resources I have personally used. They all deliver better value that some of the resources I paid for.
Let's start with R
1. You can't beat Udacity's real-world project based training on R for data analysis free course: https://www.udacity.com/course/data-analysis-with-r--ud651
2. There is also the amazingly rich and fully free DataCamp Introduction to R course: https://www.datacamp.com/courses/free-introduction-to-r
3. Finally, you should try out Swirl: http://swirlstats.com/students.html
Now on to Python
1. You definitely should read the official Python Tutorial: https://docs.python.org/3.5/tutorial/ . It's a short read and helps you get a very good grasp of how Python works. Don't forget to set it to the version of Python you use.
2. Then give the everly amazing Udacity course on Python Introduction a try: https://www.udacity.com/course/programming-foundations-with-python--ud036
3. Time to deep dive into Python for Data Analysis on DataCamp: https://www.datacamp.com/courses/intro-to-python-for-data-science
4. Finally, take the aspects that delight you in the comprehensive Microsoft Professional Program Certificate in Data Science: https://www.edx.org/microsoft-professional-program-certficate-data-science
And you are well on your way to becoming a proficient data analyst.
Best of luck!