Coming from a background of Ruby and Elixir (but this applies to pretty much any modern programming language) I was used a very fast and loose way of interacting with Arrays or Lists. It could look something like this:

numbers = [1, 2]
numbers.push(3)
print numbers
# [1, 2, 3]

Super simple and more importantly very ergonomic for the developer. In Solidity we have to give a bit more thought when creating an Array, mostly if we want a fixed size or dynamic array.

Fixed Size

If you know the exact size of the Array you're going to need up front, you can set it at compile time. That will ensure that the Array will never have more elements than those specified, at the cost of allocating all the necessary memory immediately.

uint8[3] memory array = [1, 2];

If you can't hardcode all of the elements then it becomes a bit more verbose to work with, as we need to tell it the index of each of the elements we are adding. It'll be easier with dynamic Arrays, but more on that later.

uint8[3] memory array;
array[0] = 1;
array[1] = 2;
array[2] = 3;

Memory vs Storage

You might have noticed that we've been adding a memory keyword to the declaration of all our Arrays so far, which means, you've guessed it, they will only existing in memory and will not be persisted. This is nice and all, but at some point we probably want to persist some of our lovely data. That's where storage comes in, it means that the Array will be stored in the Blockchain and can be accessed by any function at a later point in time.

To declare an Array to be in storage we have to do it from outside a function, in the main body of the contract, but other than that it looks exactly the same.

contract MagicData {
  uint8[3] public array;

  function populate() public {
    array[0] = 1;
    array[1] = 2;
    array[2] = 3;
  }
}

This all applies to dynamic Arrays as well, only the syntax of how we create and populate them changes.

Dynamic Size

This is the type of Array I was most used to working with in the dynamic languages I had mostly worked with before Solidity, provided it is in storage.

contract MagicData {
  uint8[] public array = [1, 2];

  function populate() public {
    array.push(3);
  }
}

See how it resembles the first example I gave that was written in Ruby? Quite ergonomic as well, but if you try this with a memory Array you'll get an error at compile time.

function populate() public {
    uint8[] memory array = [1, 2];
    array.push(3);
}

/*
Compiler run failed:
Error (9574): Type uint8[2] memory is not implicitly convertible to expected type uint8[] memory.
    |
    |         uint8[] memory array = [1, 2];
    |         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Error (4994): Member "push" is not available in uint8[] memory outside of storage.
    |
    |         array.push(3);
    |         ^^^^^^^^^^
*/

As you can see it complains that the type cannot be uint8[], but needs to be uint8[2], which is the first indicator that it cannot be initialized like this in memory and still be dynamic. The other error is even clearer, it tells us that we cannot use push on Arrays that are not in storage.

A memory Array needs to be interacted with like if it was a fixed size Array.

uint8[] memory array = new uint8[](3);
array[0] = 1;
array[1] = 2;
array[2] = 3;

Note that it has to be initialized using the new keyword and given a size. The key takeaway here is, if you want dynamic Arrays, keep them in storage.

Conclusion

We've seen how to populate Arrays in Solidity in many different ways, none of which is the best or the only right way to do it. To my Rubyist eyes, the storage dynamic version seems better, but it does usually consume more gas than it's fixed sized counterpart and even though I'm a firm believer of Sir Tony Hoare's "premature optimization is the root of all evil." statement, in Solidity the correlation of optimization and money savings for your users is much more obvious, therefore it's usually a worthwhile tradeoff.