Yakuhai
The great thing about yakuhai, or value honor yaku, is that they come with almost no restrictions.
Tanyao and Pinfu are also easy yaku to win with, but they impose conditions on all fourteen tiles in your hand.
There are almost no other yaku that clear the one-han requirement with just three tiles.
On top of that, yakuhai can be used even after calling.
In fact, yakuhai is one of the yaku that appears most often in mahjong.
If you get better at handling honor tiles, and combine them well with calling, your win rate will rise.
1. Keep Value Honors
After the deal, many players cut in the order guest wind -> value honor -> useless number tile.
But if you want to make better use of yakuhai, you should aim for useless number tile -> value honor whenever possible.
It is true that number tiles usually have more effective draws,
so the key is to identify which number tiles are truly unnecessary.
Example 1
For example, in this hand, you can cut first,
instead of breaking up .
Example 2
In Example 2, your ryanmen taatsu are already in place,
so holding is not worth much.
You would be happier if paired up
than if you simply made another meld elsewhere.
As long as the acceptance on 2m-5m and 5p-8p is good enough,
this hand should discard .
2. Yakuhai or Tanyao?
In general, Tanyao is better.
When you are calling, Tanyao is easier to complete, and it also combines more easily with other yaku such as Pinfu.
Example 3
Tsumo 
Dora
In Example 3, it is better to drop
and shift to Tanyao.
Example 4
Tsumo Dora
But in a hand like Example 4, where Tanyao is not yet guaranteed,
you should not drop .
In that case, it is better to discard either or .
Theory Summary
If the final point value is the same, a guaranteed yaku is better than an uncertain one.
3. About Calling
Basically, it is fine to call on the first copy.
People often say that value tiles should only be called after the second copy appears, but I think that is an old-fashioned idea.
First, even a cheap win still cuts off other players' chances,
so it has value beyond the raw points.
Second, in red-five mahjong, even after you call,
you can still draw red tiles later and turn the hand into a high-value win.
And most importantly, modern players place a much heavier emphasis on speed.
If you wait for the second call, many hands simply do not make it in time anymore.
In fact, even strong players often call on the first copy.
Do not let old value judgments trap you into thinking that first-call yakuhai is ugly, or that you should always be greedier about yaku.
In modern mahjong, first-call yakuhai is the default.
That said, if the hand is already strong enough to go closed, as in Example 5,
or if the hand is too poorly connected, as in Example 6,
then you should not call from the very first copy.
Example 5
Example 6
Theory Summary
There are usually only two times to wait for the second call on yakuhai: when your hand is very good, or when your hand is very bad.
Original Japanese page: http://beginners.biz/teyaku/teyaku03.html