Noun 1 + 是 + Noun 2 - Expressing that Noun 1 "is" Noun 2 with "Noun 1 + shì + Noun 2" (是 is only used to link two nouns, it cannot be used to link a noun and an adjective)
今年的1月1日是星期三。

Statement 1，也 + Statement 2 - Expressing "also" to link two statements with "Statement 1，也 + Statement 2"
今年的1月1日是星期三。这也是新年的第一天，人们都很高兴。

Proper Noun / Noun / Pronoun + 的 + Noun - Expressing a possessive particle, relationship or link with "Proper Noun / Noun / Pronoun + de + Noun"
这也是新年的第一天，人们都很高兴。
他们这样做是想欢迎新年的到来。

第 + Number + (Measure Word) - Expressing numerical sequence with "dì + Number + (Measure Word)"
这也是新年的第一天，人们都很高兴。

Noun + 们 - Expressing the plural form of a noun with "Noun + men"
这也是新年的第一天，人们都很高兴。

Subject + 都 + Adj. Phrase - Expressing a descriptive statement with emphasis that it applies to "all / both" of the subjects with "Subject + dōu + Adj. Phrase"
这也是新年的第一天，人们都很高兴。

Noun / Pronoun + 很 + Adj. - Expressing "very" or to link a noun or pronoun and an adjective with "Noun / Pronoun + hěn + Adj." (sometimes the 很 is translated as "very" but often it is a link between a noun and an adjective)
这也是新年的第一天，人们都很高兴。

在 + Place - Expressing to be located in or at a certain place with "zài + Place"
在中国南宁，那天有3000多人一起在冷水里游泳。

这 / 那 + Measure Word + Noun - Expressing "this… / that…" with "zhè / nà + Measure Word + Noun"
在中国南宁，那天有3000多人一起在冷水里游泳。

Place + 有 + Object - Expressing the existence of an object in a certain place with "Place + yǒu + Object" (similar to "there is" or "there are")
在中国南宁，那天有3000多人一起在冷水里游泳。

Number + 多 - Expressing a number in excess with "Number + duō"
在中国南宁，那天有3000多人一起在冷水里游泳。

Plural Subjects + 一起 + Verb / Verb Phrase - Expressing that two or more subjects perform an action "together" with "Plural Subjects + yīqǐ + Verb / Verb Phrase"
在中国南宁，那天有3000多人一起在冷水里游泳。

(在)...里 - Expressing "in / inside…" with "(zài)...lǐ"
在这些人里，有大人，也有小朋友。

这些 / 那些 + Noun - Expressing "these / those…" with "zhè​xiē + Noun"
在这些人里，有大人，也有小朋友。

最 + Adj. / Verbs of Feeling - Expressing "most / the most / -est" with "zuì + Adj. / Verbs of Feeling"
他们最大的79岁，最小的8岁。

Adj. + 的 (+ Noun) - Expressed to link an adjective describing a distinguishing feature to a noun with "Adj. + de (+ Noun)" (noun can be omitted when obvious or has already been mentioned)
他们最大的79岁，最小的8岁。

Subject + Number + 岁 - Expressing the age of the subject with "Subject + Number + suì"
他们最大的79岁，最小的8岁。

Subject + 想 + Verb (+ Object) - Expressing "would like to" with "Subject + xiǎng + Verb (+ Object)" (negative formed with 不想)
他们这样做是想欢迎新年的到来。