According to Chinese Language grammar wiki:
Used with Nouns
一点 (yīdiǎn) can be placed before a noun to mean "small quantity," like 一点水，一点钱 while 有点 (yǒudiǎn) can't be used this way.
Used with Adjectives
有点 (also 有点儿) is placed before an adjective, and it usually expresses something that the speaker doesn't want or his own negative feelings about something.
一点 (also 一点儿) cannot be placed before an adjective. Instead, it is placed after adjectives. The adjectives that can be used are particularly limited. 一点 is often used when comparing, or expressing speaker’s wish or expectation.
However, how can you use these words when you want to use it on verbs? For example, in order to add a little to the following sentence:
Which is the correct adverb and in what position should it be placed?