Taking Inventory
Press 'e' to open your inventory.
This is the first Achievement you should try to get, and defiantly the easiest.

As you see the game will let you know what you need to do for this one. Im sure this also servers as a guide to help new players a bit. The default button for the inventory is 'e' so the message will display whatever button you have the inventory mapped to.
So to get the achievement, simply press the button it tell you to, and open your inventory.
Yay for your first achievement.
Getting Wood
Punch a tree until a block of wood pops out.
For this achievement, you will need to gather just 1 log. So first lets find ourselves a tree:
Now hold the Left mouse button to begin punching the tree. Hold it down until the tree breaks, and a little log pops out:
In order to get the achievement, simply walk up to the little mini log, and pick it up. (It will automatically pick it up once your close enough to it)
Benchmarking
Craft a workbench with four blocks of wooden planks.
Another simple achievement, which involves crafting a workbench.
So now that we have our wood from the last achievement, lets craft it into some wooden planks. To do so, open your inventory and put your wood plank into your 2x2 crafting area. You will get 4 wood planks out of it.
After that, take your new wood planks, and drop one (right click while holding a stack to place one item from that stack) and make a square formation as shown:
This is how you craft a crafting table. To get the achievement, simply pick up your new crafting table, and put it in your inventory.
Time to Farm!
Use planks and sticks to make a hoe.
For this one you will need at least one log, and a workbench. Go on ahead and turn your log into 4 wood planks.
Open up your inventory and make some sticks. To make sticks, simply put one wood plank over another. You will only need to do this once, as you need your other two wood planks to actually make the hoe.
Now lets get our crafting table and set it down somehwere. Simply put it in one of your inventory slots, and then right click to place it somewhere.
Right click on your crafting table to bring up the crafting screen. To make a how, you need to put one stick on top of another, and then 2 wood planks to form an upside down "L" shape, like so:
Simply grab your hoe to put it in your inventory to get this achievement.
*Keep in mind that you can use other materials besides wood planks to make this tool. Wood is the easiest to find though.
Bake Bread:
Turn wheat into bread.
This achievement is going to take a bit of work, so get ready. Our first step is to find some seeds. So lets get our new hoe ready, and begin right clicking on grass to till it, to look for seeds.
After a while you should get some seeds that will pop up. You will need around 3 for this, so it is preferred if you get at least that much.
Now you will need a place to plant them. You can use the spaces that you just tilled to plant them in, but it will go faster if you plant them next to water like so:
Get your 3 seeds out, and right click on farmed land to plant them.
Now comes the process of waiting for them to grow. To speed things up, you can use bone meal and right click on the crops to make them grow instantaneously.

WAIT UNTIL THEY ARE FULLY GROWN AS SHOWN TO HARVEST THEM.
To harvest your wheat, just click on your fully grown crops to get some wheat.
Now to make some bread. So lets go back to our crafting table, and arrange the 3 wheat in a line as shown:
Upon picking up your bread, you will get the achievement.
Time to Mine!
Use planks and sticks to make a pickaxe.
This is another simply achievement that involves getting yourself a pickaxe. So to start off, you will need 2 logs for this:
Turn your new logs into 8 nice little planks:
Then you will need to get yourself 1 stack of sticks. (Just 4 sticks)
To craft your pickaxe, make a T shape as shown:
As usual, picking up your new item will give you the achievement.
Getting an Upgrade:
Construct a better pickaxe.
This achievement simply calls for upgrading from a wood pickaxe, to a stone one. To do this we are first going to have to find some stone. Stone usually generates around 3-6 blocks beneath dirt. Meaning if you can find a big hillside, and dig straight into it, you will find stone pretty quick. I got lucky and only had to go 1 block before finding my stone.
Use your brand new pickaxe to whack that block to get some stone. You can use your hands for this, it will just take longer.
For this achievement, you just need 3 stone pieces, so once you have that return to your work bench.
Once you open your work bench, craft another pickaxe in the same fashion as the first, except this time use stone:
As usual, grab your pickaxe to get the achievement.
Hot Topic
Construct a furnace out of eight stone blocks.
This one is pretty simple, as it just requires us to make a furnace.
Instead of digging into a wall, I decided to go down to get my stone.
Use your new Stone pickaxe to gather 8 stone.
After getting your 8 stones return to the surface and get back to your crafting table.
Align your 8 stone in a circle like shown:
Grab your new furnace to get this achievement.
Acquire Hardware
Smelt an iron ingot.
This one, while not hard, may take some time. To start, we will need out trusty pickaxe. Once you have it ready to go, go on ahead and start mining your way downwards.
After a while you will come across a brown like ore like this:
You will NEED TO USE YOUR STONE PICKAXE TO MINE THIS ORE. If you are still using a wooden one, go back and make a stone one. Come back and mine it. You will not need more than one for this, but its good to go on ahead and collect it all for later use.
After returning to the surface with your new iron, you will need to smelt it to get an iron ingot. So get you new furnace out and place it somewhere like this:
Now in order to smelt, you will need a fuel. I used a wood plank, but you can use sticks, saplings, coal, and a bucket of lava.
After you have placed your iron in the top box, your fuel will be consumed and the smelting process will begin.
Once it gets done, you will find your new iron ingot waiting to be grabbed:
Grabbing it, will of course grant you your achievement.
The Lie
Make a cake.
This one is probably going to be the hardest one you have done yet.
So we will start off by planting 3 seeds, for the 3 wheat we will need.
Next we are off to find some reeds (Also known as Sugar Cane). Reeds are tall green plants that grow in 3 (sometimes 4) block high formations
near water. So walk down some beaches until you find some. You will only need two for this recipe.
After we have collected our reeds we need to make some sugar. To do this, simply put the reeds in your crafting area:
Now that we have our reeds, its time for the next ingredient. Milk. We will need 3 buckets of milk, so its time to find some iron. Use whatever mining technique you like best, but you will need 9 pieces of iron. Throw them in your furnace to smelt them into some Iron ingots. To make a bucket, make a 'v' shape like shown (I already made the other 2):
Now that we have 3 buckets, its time to find some cows:
To get milk from the cow, simply hold up a bucket, and right click on the cow. You can use the same cow for all three buckets. Make sure you have all three, as sometimes cows dont seem to give milk.
Now comes the time consuming part. Getting the egg. To get the egg you will need to find a chicken:
After you get your chicken, follow him around for a while until he drops an egg. Chickens drop eggs every 5 minutes or so, so you will be following him for a while. Unless you get lucky of course.
Now that we have most of our materials, lets go back to our farm to collect the wheat that we need. Remember, bone meal can be used to speed growth up.
Now that we have all the materials, lets head back to our crafting bench to make cake. Align your stuff as shown:
As usual, picking the cake up and putting it in your inventory will give you the achievement. Note that your buckets are still usable.