によると

According to
Information Source + によると

によると is an expression used to indicate the source of information. 
It may be used with people, dictionaries, websites, etc.
Due to marking an information source, it is commonly used with words like:
ということだ、とのことだ、みたいだ、らしい、そうだ, etc.

Examples

• 天気予報によると、今日は降らないみたいだ.
  According to the forecast, its not going to rain today.
  
  
• 辞書によると、寿司みたいだ
  According to the dictionary, its (a kind of) sushi. 
  
  
• 彼女によると12月が一番いそがしい
  According to her, December is the busiest. 
  
  
• 子供によると、ハンスはいいひとだ。
  According to the children, Hans is a good guy. 
  
  
• 医者によると、心配することじゃないみたいだ
  According to the doctor, its nothing to worry about. 
  
  

によれば

You may sometimes hear this expression as によれば.
There’s no difference.
However, によると is more common.

Grammatically, the difference between conditional と and ば may come into play, but its so minor it really doesn’t matter.

• 彼によると
  When you ask him…
• 彼によれば
  If you ask him (specifically) then…
  
  

ところによると

From what I heard/Saw/Etc.
Plain form verb + ところによると

Sometimes, you may hear this expression with a ところ in front of it.
This allows it to connect to verbs and merely expresses its what you heard, or what someone said, etc.
You can think of ところ here as “こと”.
Past tense, present tense, and present progressive tense are fine here.

Examples

• 彼が言ったところによると、アメリカに帰るようだ。
  Based on what he said, it looks like he’s going home next year.
  
  
• ニュースで聞くところによると地震があったみたいだ
  From what I hear on the news, there was an earthquake. 
  
  
• 彼を見ているところによると、元気なさそうだ
  From what I see of him, he doesn’t look healthy.