You can start making basic "redstone" devices as soon as you have enough wood to make a door and a pressure plate: make the door and the pressure plate, and put them next to each other. Voila! Your first "redstone" device without needing any redstone.
If you want to start getting into more complex devices like flip flops, you need redstone dust: you can find it by mining redstone ore deep underground: 16 layers above bedrock or lower (sea level is at the 64th layer).
The best way to learn how to make redstone devices like flip-flops is to watch the myriad of tutorials on YouTube: figure out what you want to make, search for a tutorial on how to make it, and repeat it1.
For example, Rolf-David's tutorial shows you how to build a basic T Flip Flop:
The basic flip flops (and most redstone devices) are pretty simple, but aren't very efficient because of the way redstone works: they take up a lot of space and because power doesn't travel instantly across redstone, larger circuits are incredibly slow.
So what people have been doing is exploiting buggy implementations of blocks not intended for redstone circuitry to make them smaller and faster. Etho is probably best known for exploiting what's called the "block update"; a quirk of Minecraft where blocks send power when they update their status:
For the most part, if you never got into advanced features like this, you'd still be fine.
Note 1If you want a more comprehensive education on Redstone, there are couple of channels that focus on it pretty heavily: Etho's Lab and SethBling probably the two biggest ones. Etho's Lab is more "Let's Play"-ish (although he does do stand-alone tutorials from time to time), whereas SethBling is pretty heavily focused on tutorials.