Over the years, I've enjoyed attending trivia nights at local pubs and schools. It's fun to try to stretch your thinking, and of course, fun to meet up with lots of interesting people. I can't tell you how many times though, I've been asked about collective nouns for words in English.
"Group" is a common enough word, but if you use it all the time, you won't be considered very literate. While you can say "There is a group of dogs", it's more correct to say "There is pack of dogs". Instead of "There is a group of sheep", you say "There is a herd of sheep".
A similar thing applies to individual items within a collection. We could say "This is a paper", the meaning isn't the same as if we say "This is a piece of paper". The word "piece" is a type of word that's used to measure part of a collection i.e. it's a "measure word". "Three coffees" isn't quite as meaningful as "Three cups of coffee". If you said "Three pieces of coffee", you'd probably get strange looks.
A similar thing happens in Chinese, but it's even more pronounced. That's most likely because it doesn't have separate words for singular and plural nouns like we do. We know that when we say "goose" we mean one, and by "geese" we mean more than one.
The general word for a unit is 个 (gè). While you could use it for almost anything, you'd sound like you can't speak properly. So part of the trick is learning a bunch of measure words. So, instead of
那是一个狗。(Nà shì yīgè gǒu.) or "that is a dog"
you'd instead say 那是一只狗。(Nà shì yī zhǐ gǒu.)
or even 那是一条狗。(Nà shì yītiáo gǒu.)
Note that the measure word for dog is 只 (zhǐ) but 条 (tiáo) is also a generic measure word for long skinny things. It can be used for dogs, but also applies to snakes, fish, etc.
So, previously I mentioned "a piece of paper". That would be: 一张纸 (Yī zhāng zhǐ) In this case 张 (zhāng) is the measure word or 量词 (Liàngcí) for paper (纸). So three pieces of paper is: 三张纸 (Sān zhāng zhǐ)
And while it's important to learn that 船 (Chuán) is a ship or boat, it's just as important to know that five ships is 五艘船 (Wǔ sōu chuán) where 艘 (sōu) is the measure word for ships. And two books is 两本书 (Liǎng běn shū) where 本 (běn) is the measure word for books. One computer is 一台电脑 (Yī tái diànnǎo) where 台 (tái) is the measure word for computers.
By the way, the word computer 电脑 (diànnǎo) is wonderful. It's literally "electric brain".
This is a pretty good reference for these measure words:
I'll write more soon on the best methods for learning. If you want to get a taste for it in the meantime though, my current favorite site is iTalki, and my favorite teacher by far is Amy He. If you decide to try it, click here and it's cheaper for both you and me.