Go to Electronics Experiments (James Calvert, Associate Professor Emeritus of Engineering, University of Denver)
On the pages of this site you can find some interesting descriptions of electronics experiments. Calvert gives some suggestions what you might try and also explains the foundations, but you already need a solid background (not so much in mathematics as Calvert says on the Preface page, but you should already know the fundamental devices and circuits of electronics). As a beginner, you should better take a look at Lessons In Electric Circuits (allaboutcircuits) and the experiments that are described in Volume VI.
On the 2nd page “Your Laboratory” Calvert gives some good advice about the minimum equipment of a small personal electronics lab and some tips for breadboarding (you can find more tips on my Breadboarding and Prototyping page), some hints from experience and a list of sources for electronics components. The 3rd page “Measuring Currents” gives a short introduction to linear circuits – for longer introductions please take a look at the resources on my basic linear circuit analysis page.
The other pages are mostly independent of each other and you can just select the topics that interest you most. In a nutshell, most of the first 50 pages cover analog electronics. The next 30 pages are mostly about digital electronics (including microcontrollers and some information about assembler programming) but also include some more topics from analog electronics.
Some of the experiments use tubes, or other devices that require dangerously high voltages. Unless you already have experience with them, or you can get help from someone who has, I recommend that you stay away from them. At least you should take a look at this introduction to Electrical Safety before you try any of these experiments.
Calvert has also written several pages about electrical topics. Furthermore many pages about diverse areas of science and technology. I found that the most interesting of these are the pages about Physics and Mathematical Physics.
You may also be interested in some other recommendations for resources on practical analog electronics.
Wise Warthog Site Overview:
General: Forums, Tips on how to seek Advice
Practical Electronics: Books and Other General Resources, Troubleshooting, Introductions to Oscilloscopes, Breadboarding and Prototyping
Foundations: Basic Linear Circuit Analysis, Analysis and Design of Electronic Circuits, Introductions to Analog IC Design, Circuit Simulation with SPICE
Devices: General Op Amp Resources, Op Amp Applications, Resistors, Capacitors, Diodes, Bipolar Junction Transistors
Application Notes: Analog Devices Seminar Notes, Columns and App Notes by Bob Pease, App Notes by Jim Williams, E-books and App Notes from Texas Instruments
Mathematics: Complex Numbers, Calculus, Mathematics for Physics and Engineering
Wise Warthog - Learning Resources
for Analog Electronics and more