Minecraft – How to make a chest open with redstone or command

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 1}If 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.

In order to drop the contents of a chest, it must be actually destroyed. The only way to destroy specific blocks using redstone devices is to use pistons to accomplish one of these things:

• Remove the support of a block that is attached to another block.
• Attempt to move blocks such as plants and torches, which drop instead of moving. (Interestingly enough, this property doesn't seem to relate to anything else — most such blocks are insta-break and washed away by water, but e.g. pumpkins aren't; conversely, attached blocks such as rails and trapdoors may be moved as long as the destination also has a valid attachment point.)
• Remove the support of a falling block and drop it onto an invalid location.

Since chests have none of these properties, your idea of TNT is probably the only way to destroy chests on command.

However, given your purpose, you could probably effectively use droppers (or dispensers) instead, and have a completely reusable system with no blast shielding. A single dropper holds only 9 stacks, but you can expand its capacity by connecting it to a chest via a hopper; this is limited by the hopper's transfer rate, but multiple parallel chest/dropper systems will take care of that.

Simply connect a suitable number of droppers, facing a water stream or open shaft above you, to a single redstone clock, and adjust the period of the clock so that you get the appropriate rate of paper output. Etho's Trading Hut (thanks @BlaXpirit for the link) is an example of such a construction (made in the pre-hopper days, so it uses many dispensers alone); it's very large, but the size only depends on how much paper you want to trade.