The word 点 (Diǎn) is particularly useful. It basically means "a dot" like made with a writing brush, and from that, it means "a little bit".
I previously discussed how northerners (and Beijing folk) put "r" sounds on the end of many words. This is another one. So they'd often use 点儿 (Diǎn er) which is pronounced a bit like "dee-arrr".
There are two basic ways that点 gets used though.
One common use is 一点 (Yīdiǎn). The first character basically means "one" and this pair of characters is commonly used for "a little".
Another common use is 有点 (Yǒudiǎn). The first character in this case means "have" and this pair of characters also tends to mean "a bit".
So then, which is used when?
Let's see some examples:
今天我有点忙。(Jīntiān wǒ yǒudiǎn máng.) This means "today I'm a little busy". When 有点 is put in front of adjectives like "busy", it implies more of a negative connotation. It's almost like "today I'm a little too busy".
一点 can't be put in front of adjectives but it can be put after them.
请开快一点。(Qǐng kāi kuài yīdiǎn.) is "please drive a bit faster".
When 一点 is put in front of a noun, it means "a little" as a quantity.
请喝一点水。(Qǐng hè yīdiǎn shuǐ.) is "please drink a little water".
Slightly Tricky Negative Rules
There are also some rules for negatives. The most common "not" words are 不 (Bù) and 没 (Méi). (We'll talk another day about how they differ). But if you are putting 点 in front of either, it should be 有点.
他有点不高兴。(Tā yǒudiǎn bù gāoxìng.) is "he is a little unhappy".
However, if the sentence has 都不 (Dōu bù) or 也不 (Yě bù), then 一点 should be used instead.
她一点都不喜欢这音乐。(Tā yīdiǎn dōu bù xǐhuān zhè yīnyuè.) is "she doesn't like this music at all".