Minecraft is a very interesting and unique game. There is no end to the game nor is there a point where you are officialy better than any other player. It has no storyline or direction. You are placed in a randomly generated world made up of blocks with nothing but your bare hands. From here you can gather some basic materials such as wood which can eventually be used to craft tools that can get stronger materials such as stone, iron, or even diamond. You mine away at everything in site searching for valuable materials or amassing large quantities of cheap common materials. But collecting is not the point of Minecraft, it is using these materials to build. What you can build is as far as your imaginiation takes you. Limitations live only in our minds. But if we use our imaginations, our possibilities become limitless.
In minecraft there is no set goal, you make your own and work towards them. Whether it be a nice looking summer home overhanging a cliff, or replica of a NASA space shuttle.
If I had to give two tips for enjoying Minecraft, it would be these: 1) Do not rely on fire to clear away forests unless you want your game world to look like the Vietnam War, and 2) Give yourself a project. You have to find your own entertainment...
-Ben Croshaw
There are relatively few materials in minecraft given the amount of things you can do with them. But they can in general be catiorized into 5 groups. Those are: natural, grown, ores, liquids, and mob drops. These materials can be used in combination to make elaborate structures.
Crafting is an essential part of minecraft that takes place almost immediately after you enter the game. Crafting is done by opening up one's inventory and arraning collected resources in a certain order over a 2x2 or 3x3 grid or by smelting one material into another. Crafted items typically cannot be reverted back into their base materials. There are many more crafted items than crafted materials although some natural materials can be crafted- for instance smelting cobblestone creates stone. Tools are a crafted material that are generally need to actually gather more materials. Pickaxes for rock type materials, shovels for dirt like materials, and axes for wood. Some additional examples of crafted items are doors (which open and close on a 90o arch), steps, furnaces, chests, glass, and even TNT.

This is an example of an Iron Pickaxe being crafted out of 3 iron bars and 2 sticks inside the crafting table
Redstone quite has possibly more potential uses than all other materials in the game. Gathered from Redstone Ore it functions as eletrical wire. Redstone can also be crafted into a power sources called a redstone torch. Redstone torches have some very interesting properites which when used in combination with other redstone torches or redstone wire can produce some very interesting results.
In certain configurations such as when redstone wire runs into the back of a block that has a redstone torch on the front side redstone tourches will switch thier state from "on" to "off" depending on on the signa recieved from the wire. If the redstone wire is powered the redstone torch will become undpowered which could turn power off to redstone wire and other torchs. Using this property it is possible to make simple logic gates and in some extreme examples these gates can be combined to create a fuly functioning computer within the game world.A complete list of redstone circuits
Redstone's primary use to your average user however will not be in creating an in game calculator however. Its primary use is to provide power to things such as doors which when provided power from a permanent source such as a redstone torch or a temporary one such as a button or pressure plate will open and close when their power is taken away. This can be used to make a door that can be opened only from the outside or to alert a user that someone has entered through a door.

This is a quick and basic design that I constructed to show off one way that redstone can be used. When the pressure plate to the right is activated it opens the door and provides the neccessary component to an AND_Gate that allows power to be fed back into a the repeater and continue powered the door and the AND_Gate. When the pressure plate to the left is activated the AND_Gate loses one of the neccessary imputs and ceases to function reverting the door back to the closed state. In short once the right pressure plate is activated the door will remain open until the left pressure plate is activated.