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? Put it on peaceful and voila! Your health will slowly regenerate and all aggressive mobs will disappear.
Remember the Pattern
Struggling to remember crafting patterns? 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 or metal ingots 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, 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 may dig into a crevasse or lava pit, and 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 just set it to peaceful mode and relax. (See first paragraph.)
First Night
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. After that make a pickaxe and a shovel. Decide whether you want your base to be a house (a), or cut into a mountain (b), make your base accordingly, and try to keep it as close to your spawn as possible.
A. Use any old block (preferably sandstone) 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 just one piece of coal to burn 8 blocks of tree wood, and those 8 blocks of tree wood turn into 8 charcoal, which function exactly like coal, if you have enough time before sun sets, you should get some more wood to make more charcoal, if not, you can use 1 charcoal for 4 torches which can illuminate your house. (DON'T USE 'FIREPLACES' IN A WOODEN HOUSE!)
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's any coal jutting out. Then get some stone, shouldn't be hard, make a furnace, get your piece of coal, put it in the furnace 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'
Second Night
A/B. On your second day your main focus should be more charcoal.
Third Night
A/B. And on the third, gather much wood/stone. after that, you can make a couple houses to stay in (nearby your spawn.) If you plan on moving across ocean, make a boat if it's far away; and try making a base on an island.
Mining
A. Make sure you have a lot of picks, and at least 16 torches. Slowly mine a big stairway to bedrock, lighting your way with the torches as you go. If you plan to have 1x2x2 paths leading of the side of the stairway bring as many torches as you can hold.
B. Make a 1x2x2 doorway in the back of your home. After that easy step, make a huge room and have several difference ways to mine. Low and high, left and right, your sure to hollow out that mountain soon, getting much coal and iron.