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I've just started learning kanji but I don't understand what part of kunyomis
I should memorize.

This is the first kanji in kanjidamage.com:

一

Its kunyomi is this:

ひと*つ

According to howto page of the kanjidamage.com :

```

    In KUNyomi, the asterisk (*) shows where the kanji ends and the okurigana begin. For instance,
    if the kanji is 食 and the kunyomi is た＊べる, then it's normally written 食べる.
    
```

So, shall I memorize the kunyomi as `一 = ひと` or `一=ひとつ`? Do I need to memorize
that it is actually used as 一つ?

I've googled but found nothing about this.
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2015-01-02T08:13:13.733
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kanji
What part of the kunyomi must be learned?
You should memorise that 一つ is pronounced ひとつ. It's certainly not the only
compound where 一 appears, so _don't_ memorise that 一 "is actually used as 一つ".
一 is also pronounced ひと in other contexts, such as 一人{ひとり}, so if anything,
you should memorise that the kun'yomi of 一 is ひと.
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2015-01-02T09:54:46.197
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This is a complement to the other answer.

kun'yomi do not exist by themselves per se. Instead, they exist in words (of
which one possibility is a word identical with the kun'yomi).

So what you want to do is memorize words including which part is the kun'yomi
and which part is the okurigana.

As/if your fluency for the language increases, you will be able to better
intuit when to use what reading (regardless of whether that reading is kun or
on) in what you encounter. If you have access to native speakers, this is what
they do when trying to read unknown words or phrases. In the same way that
native AmE and BrE speakers know roughly how to read what they encounter in
English.

* * *

What might be helpful to understand is that kanji are used in roughly three
ways in Japanese:

  1. In Chinese (or Chinese-style) vocabulary which generally use the on'yomi to read one character or a compound of characters.
  2. As a way to write down words originally native to Japan (or those that are treated as such).
  3. As a way to write down foreign words based on readings of the characters. (A system that was formerly more common, e.g., 仏蘭西 = France, 亜米利加 = America)

Here's two example sets. The character 忙 is used both for

  1. The Chinese imported vocabulary term [繁忙]{はんぼう}
  2. To write down the native Japanese word [忙]{いそが}しい

尻:

  1. [not common]
  2. The native Japanese words [尻]{しり} and [尻目]{しりめ} and [尻尾]{しっぽ}. Also,the place name [野尻]{のじり} and many others.
  3. To write down the foreign ainu word ri shiri [tall island] --> [[利尻島]{りしりとう}](http://ja.wikipedia.org/wiki/%E5%88%A9%E5%B0%BB%E5%B3%B6)

正:

  1. [正直]{しょうじき}, [正立]{せいりつ}, ... basically two on-yomi しょう and せい
  2. [正]{ただ}しい, [正]{まさ}しく, and a plethora of readings in names
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