Usually the reason we design things is so that we can make something or accomplish something. Our design usually has the constraints of limited resources - time, money, technology, safety, skill, etc.
It appears that what you want to accomplish is learning so that eventually you have knowledge, skills and experience. You may want to take that and actually do something - design a radio or audio amplifier - or you may be quite satisfied with just the knowledge.
You need some knowledge and skills to start with and you've indicated that you have some. Adding to those skills certainly would help (courses, degree, etc) or you simply dive in with what you have and see how it goes. You will learn by doing - and some 'doing' is essential to any knowledge or skill building endeavor. Whether or not you'll learn the right things by diving in right away remains to be seen. If you were to follow some tutorials or publications or self-teach courses it would seem that the likelihood of learning the right things is greater. If you are anxious to start doing something then do a little research on the things you can make with a 741 or similar op amp (you said you were familiar with them). Copy designs- build them, test them, change them. Experiment to see how theory compares to actual results - to the extent that you can with the instruments on hand. When you feel you undertand - then move on.
It does help to have a specific area of interest in mind - audio amplifiers might be one area, robotics are another. Be careful not to fall into the trap of wanting to do everything all at once. Don't start and expect that in one project you'll be successful at designing and building a high power, high quality stereo amplifier. Start with a single channel amp and be happy if you get anything out of it at all - walk before you run!!
Books - Radio Shack has some good beginners books. ARRL and RSGB have great publications for radio amateurs - many who want to learn electronics. My favorite is Paul Scherz "Practical Electronics for Inventors." Don't overlook the 50 in 1 or 200 in 1 kits that appear to be toys for children - lots to be learned. You can build the stuff - then reverse engineer to see why it works. Lots of learning there.
Anyway, enough babble. I hope this helps.