The Attributive
An attributive is a word or phrase that decorates or modifies another term. The modified word may be either the subject or object. For instance,

他妈妈要去上班了 (tā māmā yào qù shàngbān le)。His mother is going to work. (The pronoun "他" is the attributive and is placed before the subject "妈妈".)
这只狗是Holly的 (zhè zhī gǒu shì Holly de)。This dog is Holly’s. (The attributive "这只" is before the subject.)
我买了一个西瓜 (wǒ mǎi le yígè xīguā)。I bought one watermelon. (The numeral-measure word phrase "一个" is the attributive and is before the object.)
那是明天考试的试卷 (nà shì míngtiān kǎoshì de shìjuàn)。That is tomorrow’s text paper. (The noun "明天" is the attributive and is before the object.)

An attributive should be placed before the modified word. Any kind of notional word or phrase can act as an attributive. The structural particle "的" (de) is often placed after an attributive. In the examples above there are instances of a noun, a pronouns, and a numeral-measure word phrase acting as an attributive. Below are examples of other kinds of words acting as the attributive.

那辆车上有许多空座位 (nà liàng chē shàng yǒu xǔduō kōngzuòwèi)。There are lots of  empty seats in that car. (The adjective "空" acts as the attributive.)
他有三个弟弟 (tā yǒu sān gè dìdì)。He has three younger brothers. (The numeral "三个" acts as the attributive.)

Some attributives must be followed by the structural particle "的", some attributives cannot be followed by 的, and some may optionally be followed by "的".

Do not use "的" in the following circumstances:
When the attributive is a noun and describes a quality of a person or thing

制定节日 (zhìdìng jiérì) A designated holiday
销售经理 (xiāoshòu jīnglǐ) A sales manager

The attributive is a noun in a set combination
南京大学 (nánjīng dàxué) Nanjing University
首都机场 (shǒudū jīchǎng) Beijing Airport

When the attributive is a pronoun: and it expresses a family relationship or an organizational unit; it is "这" (zhè) or "那" (nà) and appears in front of a numeral or measure word; or it is "什么" (shénme) or "多少" (duōshǎo) and appears in front of a noun

这把椅子 (zhè bǎ yǐzi) This chair
那几个人 (nà jǐ gè rén) Those people
多少钱 (duō shǎo qián) How much money?
什么意思 (shén me yìsi) What do you mean?

When the attributive is an adjective:
红叶 (hóngyè) red leaves
长城 (chángchéng) the Great Wall

The structural particle "的" must be used in the situations below:
The attributive is a noun expression a possessive relation, time, or place

我的鞋子 (wǒ de xiézi) My shoes
去年的日历 (qùnián de rìlì) Last year’s calendar
后面的人 (hòumiàn de rén) The people behind

Adjectives acting as attributives when emphasizing decoration of the modified word, disyllables decorating monosyllables, duplicated forms:

可怜的人 (kělián de rén) A poor man
高高的建筑 (gāo gāo de jiànzhù) A tall building

Verbs acting as attributives
辩论的话题 (biànlùn de huàtí) The subject debated

Subject-predicate phrases acting as attributives
专家用的办法 (zhuānjiā yòng de bànfǎ) A method used by experts

Coordinative phrases acting as attributives
这个月和下个月的钱 (zhè gè yuè hé xià gè yuè de qián) The money for this month and next month

Endocentric phrases acting as attributives
很漂亮的裙子 (hěn piàoliàng de qúnzi) A really beautiful skirt

Phrases of locality, appositive phrases, set phrases, and prepositional phrase acting as an attributive
我自己的钱 (wǒ zìjǐ de qián) My own money

"的" can be optionally used in the following situations:

Dissyllabic pronouns acting as an attributive decorating monosyllabic collective units
咱们（的）孩子 (zánmen de háizi) Our child

Dissyllabic adjectives acting as an attributive modifying another dissyllabic word
快乐的童年 (kuàilè de tóngnián) happy childhood

Measure word phrases that borrow a noun to express the idea of a large number
一层一层（的）山 (yì céng céng de shān) Layer upon layer of mountains

The endocentric phrases "很多" (hěnduō) and "不少" (bù shǎo)
很多（的）鱼 (hěnduō de yú) Lots of fish
不少（的）资金 (bù shǎo de zījīn) a lot of funds