Pairs (1)
(1) The head
(2) A future set candidate (if you later draw one more matching tile, it becomes a triplet)
(3) A building block of seven pairs
This page looks at pairs through those three roles.
Here, however, we focus only on role (1): the head.
The Head Forms Easily
The head is required in every winning shape, including Kokushi Musou. Unlike sets, the head is not something you normally try to build on purpose. Think of it as something that naturally appears while you keep drawing and discarding.
Example 1 
Example 1 is a hand with no head, but trying to guess here which tile is likely to pair up is highly pointless.
If any one of the 13 tile types in the hand pairs up, you get a pair.
That means 13 possible kinds of acceptance each turn,
so on average a pair appears in about 2.6 turns.
Of course, even if you draw something like ,
the chance that it ends up serving as the final head is very low.
Even so, you can see why there is no need to worry just because you do not have a head yet.
Even if the hand finally becomes a tanki wait with no fixed head,
the hand still has many possible improvements, so it is not something to fear.
Example 2 
Tsumo
At this instant, Example 2 becomes a tanki wait with only 3 winning tiles.
However, if you draw 
,
the wait improves drastically.
You could also riichi on an honor-tile wait if you judge it easy to hit.
Making the Head from Composite Shapes
We just said the head forms easily. But if you try to intentionally pair a specific tile, that is difficult.
For example, if you try to make the head with 
,
you need to draw one of the three remaining copies of .
That is basically something you should not expect.
So instead, you can use already completed sets.
Example 1 
→ Tsumo →
With this shape, drawing 
gives you the head.
That is 6 tiles of acceptance, twice as many as with an isolated tile.
Example 2 → Tsumo
→
In Example 2, either 
or 
works, for the same total of 6 tiles.
Example 3 → Tsumo →
If you use a composite shape involving a concealed triplet, making the head becomes even easier.
Here the acceptance is 7 tiles: .
The same applies if you draw and form 
.
Example 4 → Tsumo →
In Example 4, the acceptance becomes 11 tiles: ￣ ￣ .
Using completed sets like this lets you make the head much more efficiently.
Concealed Triplets and the Head
If you remove one tile from a concealed triplet, you can also make a head.
Example 5 Tsumo
In Example 5, of course you would not take a tanki wait on 
or 
.
You cut 
or instead,
and take the 8-tile wait on .
The Rule: Prioritize Sets
We said you can remove one tile from a concealed triplet to make the head, but in basic play that kind of head-fixing is done only at tenpai.
Example 6 Tsumo
Example 6 is a ryan-shanten hand with no head.
Discarding 
here is a mistake.
Making the head is far easier than completing sets.
If you decide that must be the head,
you still need to make three more sets after that.
It is much easier to aim for two sets plus a head instead.
The right play in this hand is to discard .
Example 7 
Tsumo
Example 7 is also a shape with no head.
If you break up here and fix the head first,
you take a long detour before reaching tenpai.
The correct play is to discard and lock the souzu shape in as a sequence.
As this shows, prioritizing sets over the head is a basic hand-building principle. But there are exceptions.
Example 8 
Tsumo
In a pinfu-confirmed iishanten like this, it is fine to drop 
and fix the head first.
Even if that slightly reduces the acceptance before tenpai,
it is better because the eventual tenpai shape is stronger and it secures the 1-han yaku Pinfu.
Theory and Summary
Original Japanese page: http://beginners.biz/kihon/kihon06.html