Mining for a beginner

This is quite a subjective question but in terms of mining for rare items there are two main techniques you should try:

1. Cave exploration

Find the entrance to a cave somewhere in the world. Bring a sword, a few pickaxes, a furnace, a crafting table, wood, coal, armour, a bucket of water and plenty of torches. Explore the cave, mining and lighting the way as appropriate. Press F3 on your keyboard to see your coordinates. (Edit: I didn't see that you're playing on console. For Xbox, you need to craft a map to see your coordinates. This is crafted with paper and a compass). The Y coordinate represents how high up you are in the world. In order to find diamond you should be below Y coordinate 16. If the cave network you're exploring doesn't go down that far, don't worry. Simply find another cave. In the vast majority of cases however, the cave network will extend down to around level 10, where the big lava lakes spawn. This method may not net you many diamonds but the benefit is you can find all the resources you can mine on the way down, including, but not limited to, redstone, coal, gold, iron and lapis lazuli.

2. Strip/branch mining

This is a specific mining technique designed for gaining a high yield of diamond. The disadvantage is that it is very boring and takes a long time. The basic principle is to mine a staircase down to level 12, and then start mining in branches to your left and right. This allows you to essentially explore a large tunnel by only mining a few blocks. A detailed explanation can be found here.

As to your other questions:

• Mining near water makes no real difference. Probably a bad idea to mine underneath an ocean in case you get lost and need to mine a staircase upwards.

• Villages again make no difference. They're good for trading if you can find emeralds and you can get a good amount of food from the farms but in terms of mining they make no difference whatsoever.

• See above. Level 16 and below for diamond, ~35 and below for anything that isn't iron or coal.

• Day/night makes little difference as it is dark underground and monsters will spawn at all times. At night, there may be less mobs underground since they are spawning above ground as well, and there is a cap for the number of mobs that are allowed to exist at once. It follows that there should be more mobs underground during the day. However, this is unlikely to make a huge difference, so be prepared to fight at all times.

• Do not use TNT. Blocks of TNT can destroy the blocks you're trying to mine, and will result in a very low yield of materials. It's also very expensive to use for mining as each block requires 5 gunpowder. Stick to the pick.

  Finally, if you want a lot of resources, the Fortune enchantment on your pickaxe could be of use. When a pick is enchanted with Fortune, Coal, Iron, Redstone, Lapis Lazuli and Diamond ores will drop more of their respective item per block when mined. If you want a pick to last longer so you can keep mining, the Unbreaking enchantment is useful. You may also want to look at Efficiency, which increases your mining speed.

Unfortunately no matter how far down you go the game will not generate more of a certain ore within a certain area. However you can maximize your output of ores by different strategies. For iron or coal or redstone, go caving and you can easily find stacks. For lapis and gold and diamonds and emeralds, strip mining will be your best choice, you can also find many other ores while doing so. Another advice to you would be that if you find a diamond ore while strip mining, no more will spawn in that chunk, so stop mining in that chunk, you won't find any more diamonds in it. Carry lots of torches, lots of food, and lots of iron pickaxes. (Enchanting them with efficiency helps too.) Hope this helps.

Mining on the console versions of Minecraft isn't much different from mining on the PC version.

The location or time does not matter at all, ores are generated randomly using a few minor rules for their occurrence:

• There are less ores right at the surface
• There are more common ores (iron & coal) around the middle between bedrock and the surface
• The deeper you go, the rarer the ores will get:
  • Diamonds are found very deep, around the height where natural lava fills up the cave
  • A little bit above that you find: Lapis Lazuli, Redstone and Gold

Note: I don't know if there are any differences on the actual Y-level of the ores, but it seems very consistent around the web (Sources: http://minecraft360.wikia.com/wiki/Ore, http://minecraft.gamepedia.com/Ore)

Never, ever use TNT!!!

TNT explosions have the nature of all explosions in the game: They destroy blocks and drops!
It doesn't matter how much TNT you use or how far away/near the ore you put it, it will eventually destroy your ore.
A TNT explosion might seem to drop all destroyed blocks, but it doesn't: It only has a chance of 25% of dropping the block as an actual item and all items around it will get destroyed (it deals damage to the drops and thus destroys them, much like fire or a cactus does).
(Source: http://minecraft.gamepedia.com/Explosion)