How can I learn electronics at home?
I would suggest perusing YouTube for projects that might hold your interest (this is key). Once you find one you can begin researching it to determine how complex it might be, chose an initial one that might be completed in a few days. For now, I would suggest staying away from items that need programming (connections to a PC or a micro controller) because debugging software is a bit of a distraction.

Most of the YouTube posters are quite willing to discuss their creations so you can ask them if they think their projects would be suitable for a novice.  

For almost guaranteed success, you might want to purchase a kit that comes with all the components and instructions. What could missing from these is the critical experience of blowing something up (aka letting the magic smoke out) and then figuring out what exactly happened.

Useful things to buy at the onset:  a breadboard or two, a small power supply, solid core connecting wire, and some wire cutters.

I would also recommend this:  http://www.amazon.com/Art-Electronics-Paul-Horowitz/dp/0521370957