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

In my opinion, you would better start with Tony Kuphaldt's "Lessons in Electric Circuits". There are six volumes that take you by hand from the very, very basic. It doesn't assume you know anything about electricity and electronics. Each volume talks about a topic (DC, AC, Semiconductors, etc)...

https://www.ibiblio.org/kuphaldt/electricCircuits/

What you can do is to join a forum, or multiple fora. Here are examples:

http://www.electro-tech-online.com

Not bein able to post more than two hyperlinks, two other fora are (look them up on Google):

-allaboutcircuits -edaboard

These are some of the very best you'll ever find. They've been there for a long time, so your questions have probably been answered multiple times, and you can look up the archive.

I'll recommend a website that is simply great, it offers mainly reviews and answers to questions. (Which book is better suited for beginners, why, which forum to chose, which forum is specialized in what, how can I learn.. All these questions which seem daunting and you wish to have answers too..

Look "wisewarthog" on Google. It's the first result.

Take the time to navigate through it, it's deeper than it looks.. You can find infos on books and they took a lot of time to write reviews.

It's better to start by knowing how things work first, instead of just soldering stuff together à la "cargo cult", and simply downloading a schematic/layout, etching it, drilling and then having it run work like "magic" not even knowing what each part does. So documentation before projects, in my opinion.

Also, "The Art of Electronics" is great, although I wouldn't recommend it as a first read. (But it's an absolutely great read, I agree with the poster above).

All my best,

What should I do to learn electronics at home?

take on a electronics project, find a friend who knows more about electronics than you, start learning from online sources,

What minimum instruments do I need to buy?

this is the bare minimum that could be useful for starting out.

Tools: voltmeter, diagonal cutters, pliers and breadboard/jumper wire kit

Parts: that will depend on what project you take on,