While the squares can be built in any order, it is often more efficient to begin with an outer square.
An outer square is built in three steps:
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Build a corner/edge pair
Find a corner and edge piece that have two colours in common. In the example below, we have chosen the green/orange/yellow corner and the orange/yellow edge. These two pieces can be joined together so that their orange and yellow stickers join with each other. The first step in joining two pieces is to first position them so that their colours are aligned on the same axis. The concept of alignment is illustrated below:
Aligned:  
Not aligned: 
If you click play, you will find that the aligned pieces can be joined in one move, but the unaligned pieces cannot.
It follows that once you can get two pieces into an aligned position, joining them is easy.
Practice: Use the applet below to practice joining random corner/edge pairs, or click the "play" button to reveal the solution.

It often happens that a scrambled Rubik's cube contains one or more corner/edge pairs already joined. If you find one, you can use it and continue with the next step.
Build a centre/edge pair
A centre/edge pair is built using the same technique of alignment. First, we align the edge piece with the centre piece, and then join them.
However, the difference this time is that we need to preserve what we built in the previous step. There will be a corner/edge pair floating around somewhere on the cube, and we would like to build the centre/edge pair without breaking apart that existing corner/edge pair.
Incorrect  Correct 

The usual technique to avoid breaking the corner/edge pair is to move it out of the way first.
Practice: Use the applet below to practice random positions, or click play to show the solution.

By the end of this step, you should have a corner/edge pair and a centre/edge pair intact.
Join the corner/edge and centre/edge pairs to form a square
Once you have formed a corner/edge pair and a centre/edge pair, you can join them once again using the technique of alignment.
Practice: Use the applet below to practice random positions.
