Here are some tips and little hinters for those who are new to Minecraft. Remember, however, that there are often tips under the 'Trivia' section of an item's page, and are likely to be more in-depth:
Peaceful Mode
Can't seem to figure out those zombies? Too slow for the spiders? Can't make a decent shelter without the worry of a creeper? Low on health and don't have any food? Set the difficulty to peaceful and, voila! Your health will quickly regenerate your food bar won't hurt you and all hostile mobs will disappear. This becomes very helpful when building large structures or pixel art. However, most players consider Peaceful a "noob mode".
Remember the Pattern
Struggling to remember crafting patterns? Trying to make a bucket but instead you make a minecart (and waste 5 Iron Ingots!)? Take a closer look at a pattern, like the fishing pole pattern. Take notice of how the sticks and string line up to look like a fishing pole. Many patterns follow this trait, such as doors which use two columns of wooden planks to make the rectangular shape of a door, and swords which use two wooden planks, cobblestone, iron ingots, or diamond for the blade and a stick as the handle.
Shelter Problem
Is it nearing nighttime and you haven't finished your shelter yet? In an emergency situation and need some shelter? Dig three blocks down and place a block above you, and now you're safe! You may want to expand the boundaries so you may place a bed. This method is not recommended though, as you're completely exposed to mobs as you leave. Pillar jumping is another solution. Simply make a pillar directly under you until you are out of reach from the skeleton's arrows. Or you can simply set your difficulty to peaceful mode and relax. (See first paragraph.)
First Day
Punch down trees until you're satisfied with the amount of wood you have. Turn one of the wood blocks into planks and turn those into a crafting table by making a two by two square in your inventory. After that make a pickaxe and a shovel in the crafting table. Decide whether you want your base to be a house (Option A), or cut into a mountain (Option B), make your base accordingly, and try to keep it as close to your spawn as possible.
Option A: Use any block to make a home. This should be large enough for your first night, and all of the above should be able to be finished in about 5 minutes. When you get enough stone to make a furnace, you can use two planks to smelt three wood into charcoal, the cheap version of coal. It functions exactly the same as coal, and you can craft 1 charcoal into 4 torches which can illuminate your house. Remember that wood is flammable so DO NOT use 'fireplaces' in a wooden house!
Option B: Just cut into a mountain and make a hole going in, or what-ever suits you best, then dig in the middle to make a 1x2x2 doorway and make a door, put the door in and start carving out your house. Be sure to check the mountainsides to see if there is any coal jutting out. Mine some stone to obtain cobblestone, make a furnace, get your piece of coal, put it in the furnace (1 coal can smelt up to 8 items) and smelt some wood into charcoal. Charcoal can be used like coal, make 12 torches and leave the last piece of charcoal in there for future 'charcoal smelting'. This is the most efficient way to build a house because you GAIN materials when you expand the house instead of LOSING them.
Second Day
On your second day your main focus should be more charcoal. Charcoal can come in handy when you either need some extra torches, or just need some for a furnace. Also go out and kill pigs, sheep and cows for their wool (for beds and paintings), leather (to make armour with that you put on in the inventory next to your character) and meat that you cook in the furnace(to eat when your food bar gets low).
Third Day
On the third, gather more wood/stone. After that, you can make a couple of houses to stay in (ensure it is near your spawn point). If you plan on moving across ocean, make a boat. If your destination is far away, it would be a good idea to try making a base on an island.
Mining
Option A: Make sure you have a lot of pickaxes and at least 16 torches in your inventory. Slowly mine a big stairway to bedrock, lighting your way with the torches as you go. If you plan to have 1x2x2 paths leading off the side of the stairway, bring as many torches as you can hold. When you get to bedrock go up 12 stairs (to get to the diamond lair) then mine a 1x2x infinite corridor.
Option B: Make a 1x2x2 doorway in the back of your home. After that easy step, make a huge room and have several different ways to mine. Low and high, left and right - you're sure to hollow out a mountain soon, getting hefty supplies of coal and iron.
Option C: Find a cave, make a trail of torches down it if you find any iron or coal mine it, when you reach a dead end go back collecting the torches back then go down another branch do this until you have done all the branches then go out and make a signal that you have dived the cave so you don't do it again.
Option D: You will need about 2 stacks of ladders, 1 bucket of water, a few iron(or one diamond pickaxe(s)) and a sign to make a mineshaft by mining down one block next to you until it's out of reach then directly below you because you know your safe. Do this till bedrock, place down 12 blocks by holding jump and place block at the same time then make a ladder to the top (this part can be annoying). Go back down (using the ladder for safety of death) and place down the sign at eye level. After that, you put the water down (it will float) and now you can fall down safely without the ladder. Make a 1x2x2 infinite corridor collecting resources on your way, you now have a mineshaft.
Coal Without Mining
You have made your shelter, already mined some Cobblestone and can't find any Coal to light your environment? Just make a furnace, take some Wooden Planks as fuel and burn some Wood you didn't already craft to Wooden Planks. This will get you some Charcoal which has exactly the same functions of normal Coal that is mined with a pickaxe.
Places to Build
There are some recommendations where a beginner should build and where not: Use any material you want, excepting Sand or Gravel as they are influenced by gravity (which means that they fall down if no other block is under them) or dirt, because creepers can easily blow it up. Also remember not to build your shelter on Sand or Gravel, because if it comes to your mind to dig down or make a cellar, you'll have a problem because the Sand keeps falling down on you and it will take a long time to remove it from the base.
For beginners, you might want to hollow out the side of a hill or mountain. This can be done quickly and turn into a good shelter, but keep in mind it will be harder to find your home if you wander off. A second design is to collect a lot of wood and build a wooden house. These stand out easily, look good, and function well. The bad thing is they are flammable.
The Enemy of My Enemy
Getting beaten up good by lots of hostile mobs? Remember: "The enemy of my enemy is my friend." Skeletons become hostile to each other if their arrows hit each other, and you can use the blast radius of the Creeper's explosion to injure other mobs. Other MOBS, not yourself, of course. If you happen to encounter any wild wolves on your travels, you can use a bone to tame them. Tame wolves can let off some pressure in a battle by fighting other mobs for you. If a skeleton kills a creeper you get a music disc.
Darkness
Out of Coal/Charcoal? Your hands bleeding from punching too much wood? Remember that hostile mobs require a light level of less than 7 to spawn. Use this knowledge to save some torches in your shelter. On another note, if you are still using hands to chop wood at this point, then you should seriously consider making an axe.
Second-Tier Ores
See some Redstone, Diamond, or some fancy ore? Don't use low-level Pickaxes to mine them! Remember, Wood pickaxes only mine Coal and Stone, while Cobblestone mines Iron and Lapis Lazuli. Iron mines all blocks, except for Obsidian in which Diamond has the honour of mining. Be careful - lava lakes often occur at the same level as precious ores.
Item Durability
Mining deep underground and suddenly, inexplicably, your Pickaxe turns into your hand? Is it a bug? Or is it the feared Herobrine? It's neither! It's Item Durability...or Uses! Take care to look at the 'health' of your item (the little coloured bar underneath the item) before departing on any long trips, be it exploring or mining, as the last thing you want to do is to take the long trip back home just for a Axe, or a Pickaxe. Time is precious, so try bringing along a crafting table, or stock up on tools if you have to.
To the bottom of the ravine!
Often, you will come across the top of a ravine, with all the precious ores beneath. Carrying a stack of sand (some gravel will become flint, so you may not have enough to get back up), and dropping it on a location repeatedly until you have a pillar to the bottom. Standing on the pillar and digging down until it's gone will get you to the bottom without fall damage! Another way is to dig a spiral staircase downwards till you want to stop. Then dig towards the wall of the ravine then if it is still too deep, keep on digging!
Nab's way- after collecting three iron (normally 1 node) you can craft a bucket and use water as an instant ladder. Remember to refill your bucket.