There is no easy answer to this question, and actually I do not think that self-learning can lead you very far. This having been said, self-learning the application of DFT to chemical problems requires facing two different types of knowledge, one on theoretical chemistry, and one on the implementation of the theory in a computational software suite.
So, first I would go to books & manuals. For a start, the books from Jensen and Cramer might be very useful. As for the second problem, studying the manuals is mandatory. Many software suite, for example Gaussian, have very complete official on-line resources. Only after a deep study you might start using the software. A help on practical issues can came from any of the many fora on computational chemistry, including RG and the Telegram group on computational and quantum chemistry.
The best options for you are either books or youtube. You can find several lectures on youtube from DFT code developers such as Quantum Espresso, siesta and so on. All of them usually have nice lectures to introduce you to the methodology and also hands on sessions so you can experiment by yourself.
In terms of books, I highly recommend "Materials Modelling Using Density Functional Theory: Properties and Predictions" by F. Giustino. The reason for this book choice is: Most of the DFT books were not written for undergrad/master students, and they actually tend to assume that you already have knowledge of the subject to some extent. This book was written exactly for people that are just starting to introduce themselves in DFT at the undergrad level, and is actually part of the DFT bibliography for undergrads in Oxford.
This material from a computational chemistry Course (By Crammer himself) is a great start on what there is to know about DFT. http://www1.chem.umn.edu/groups/cramer/8021/index.html
I'd say: put some effort to grasp the theory behind DFT. That'll help you a lot in selecting methods, basis sets, approximations and such. For the practical side of it, YouTube is great.