How do we "spell" Chinese characters or words?

Mandarin Chinese is a tonal language. Each Chinese character represents a single syllabic unit in all spoken variants of Chinese still exist today. Therefore it is common to have several characters correspond to the same pronunciation in Chinese.

In order to "spell" a specific Chinese character, we need to know two things in advance.

1. Which character are we talking about?
2. How to decompose this character into simpler radicals or strokes?

For the first one, we infer the proper character from the context; and most often from the Chinese word 词/詞(ci2) containing this specific character. Use of Chinese word 词/詞(ci2) to tell the right character is a common practice when one introduces his or her name.

Take famous Chinese actor/singer 张学友(張學友) for example,
he would introduce himself as following.

我姓 zhang1, 名 xue2 you3.
My last name is zhang1, and my given name is xue2 you3.

By listening to the introduction above, other person may not know the exact characters in his name. Since "尤 - outstanding", "有 - have", and "友 - friend" all correspond to the same sound "you3".
So he would say following for the clarification.

张, 张开的张; 学, 学习的学; 友, 朋友的友. (Simplified)
張, 張開的張; 學, 學習的學; 友, 朋友的友. (Traditional)
zhang1 as in zhang1 kai1; xue2 as in xue2 xi2; and you3 as in peng2 you3.

Now we got all characters in 张学友(張學友) (zhang1, xue2 you3),
how do we write these characters?

Take character 张(張) for example.
Following are two typical instructions to write this character:
弓字旁,右边一个长. Or 左边一个弓, 右边一个长.(Simplified)
弓字旁,右邊一個長. Or 左邊一個弓, 右邊一個長.(Traditional)

It has 弓 as its radical, and 长(長) on the right side. Or
弓 on the left side, and 长(長) on the right side.

Great, now we know how to "spell" and write Chinese character.
We can "spell" and write Chinese word 词/詞(ci2) in the same way since it is composed of two or more characters.

Check out here for more details on Chinese character.