(一) 点儿 is a numeral auxiliary indicates indefinite small amount, more often used orally than 些  which +/- has the same meaning; e,g, 我想买(一)点儿 or 些 东西.

有(一)点儿 is a V+O structure (动宾结构) used to explain an Adjective or Verb, e.g.

今天我有(一) 点儿 忙, or

他有点儿想开车但觉得有点儿累。

Both of them means a little

   However the difference between them:

1）有点儿 should be put in front of adjective while 一点儿 behind the adjective.

有点儿+Adj                 Adj +一点儿

2). 有点儿 usually is used to express one’s own feeling, especially something negative (example a and b).     一点儿 is used to express one’s hope(example c&d)

a. 这件衣服有点儿贵。

b. 老师说得有点儿快，我听不清楚。

c. 请你走慢一点儿。

d. 可以便宜一点儿吗？

The difference explained above is only for beginners.

  A：我去超市看见香蕉四块钱一斤，我知道市场的苹果三块五一斤？超市的苹果贵不贵?

               I went to the supermarket to see banana four yuan half a kilo. I knew the apple three yuan                    five mao half a kilo in the market.  Is apple expensive in supermarket?

  B：有点儿贵   a little expensive

  A:  超市的苹果比市场的苹果贵很多吗？  Is more expensive the apple of supermarket than the         apple of market.

   B:  不，超市的苹果贵一点儿。no, The apple of supermarket is  a little expensive.

有（一）点儿+ 形容词（adj)    超市的苹果有点儿贵。

形容词（adj）+一点儿    超市的苹果比市场的苹果贵一点儿。

”有点儿“ express your own feeling and evaluation

eg: 天气有点儿热。 The weather is a little hot.

     我的房间有点儿小。My room is a little small.

“一点儿”  is often use in comparison.

eg: 香蕉比苹果便宜一点儿  Banana is a little cheaper than apple.

     我比你高一点儿。 I am a little taller than you .

very useful

check out this video, our teacher Shasha will tell you what is the difference between “一点儿” and “有点儿”.