有点儿 (yǒudiǎnr) and 一点儿 (yìdiǎnr) both translate as "a bit" or "a little", but they are not interchangeable. 有点儿 goes before an adjective and describes how things are, usually in a slightly negative way. 一点儿 goes after an adjective or verb and talks about a small change or a small amount.
Put 有点儿 in front of an adjective to say that something is a bit too much of something: a bit cold, a bit expensive, a bit busy. It usually describes something you are not very happy about, so it is common for complaints and polite refusals. It sounds odd with clearly positive words; for "quite nice" Chinese speakers use 挺 or 很 instead.
有点儿 can also go before a feeling verb such as 想, or before 不 + adjective. It is a short form of 有一点儿, which means the same thing.
Put 一点儿 after an adjective to compare or to ask for a change: a bit cheaper, a bit earlier, a bit better than before. This is very useful when shopping and when making requests.
After a verb, 一点儿 means a small amount of something. The noun comes after 一点儿. In everyday speech the 一 is often dropped, so you will also hear 喝点儿水 or 买点儿东西.
To say "not at all", use 一点儿 + 也 or 都 + 不 + adjective or verb. This is the main way to use 一点儿 in a negative sentence. Do not use 有点儿 here.
Learners often say 今天一点儿冷 for "It's a bit cold today". This is wrong: 一点儿 cannot go before an adjective in a positive sentence. Use 有点儿 instead: 今天有点儿冷.
A simple rule: 有点儿 comes before the adjective and describes the way things are; 一点儿 comes after the adjective and asks for or compares a small difference. In a shop you might use both, one after the other.
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