Although it is not possible to enter a long explanation of Chinese grammar, there are some notable features of Chinese grammar that will help you on your way to learning Chinese. Chinese is an isolating language, which means that its morphology is limited and has very little conjugation. This is why people often claim that Chinese grammar is simplistic and easy. There are no verb conjugations and only some noun conjugations.
Chinese is a SVO language, which means, generally the syntax follows a Subject-Verb-Object structure. Of course this is easier said than done. There are some other important changes in sentence construction in Chinese, that needs to be highlighted. It places importance on time and place, as these usually go at the start of a sentence. For example: 我昨天去了北京。- This sentence means: I went to Beijing yesterday. 昨天, which means "yesterday" is placed right after 我 (I). In Chinese-Ordered English that sentence would read: I yesterday went to Beijing. Furthermore, place goes after the time word. For instance: 我昨天在家看了我妈妈 （I saw my mom at home yesterday). Here 昨天 again goes after 我 and is followed be 在家, which means "at home". Once again in Chinese-Ordered English this would be: I yesterday at home saw my mom. So remember, always add time and place in the front of the sentence.
Plurals are marked with the character 们 at the end, but this only accounts for pronouns. For example, 我 (I) becomes 我们 (we). Besides these plurals, all other plurals go unmarked, however there are different ways to express count in Chinese. This is done by "measure words". These are classifiers for an object and one adds a number in front to mark the amount. This does occur in English, for example, one can say three cups of coffee. The word "cup" is the measure word. In Chinese it would be 三杯咖啡, where 杯 would be the measure word for containers of liquid, usually a glass or cup.
Other notable features of Chinese grammar is the way it handles tense in a sentence. Verbs are not conjugated according to tense, but rather uses aspectual particles and adverbs to convey tense. For instance, in English "to eat" would conjugate to "ate" in a sentence like, "Yesterday I ate chicken". In Chinese this would be 昨天我吃鸡, literally meaning: "Yesterday I to eat chicken". 吃 is the verb "to eat". However, it does not differ in present tense, 我吃鸡. However, aspectual particles, such 过 and 了 adds a perfect tense to the verb. For instance 我吃了鸡 in English would be, "I have eaten chicken".
In the end, there are a lot more interesting things in Chinese grammar, however it should be noted that Chinese grammar is simplistic. It might be easy, if you understand it, but it is very different to English. Rather aim for brevity and conciseness in Chinese. Keep it simple.