When should I use 'to doing'?
Usually, we say someone to do something. However, there are some exceptions.
Ex
I'm looking forward to hearing from you
A theoretical approach to understanding consumer behavior.

When should I use to + doing? Plz explain it in details and with examples. Thank you!

Question

When should I use 'to doing'?
Usually, we say someone to do something. However, there are some exceptions. 
Ex  
I'm looking forward to hearing from you
A theoretical approach to understanding consumer behavior.

When should I use to + doing? Plz explain it in details and with examples. Thank you!

Answer

As Elsa says, it's when the 'to' is a preposition - belonging to the previous phrase - rather than part of the infinitive.  Here are some examples of phrases ending in 'to' which need the following verb to be in the gerund (+ ing) form:

The most common ones are:

look forward to  ( "I'm looking forward to seeing you")
be used to    ("He's not used to driving on the left")

There are also these ones:

confess to
admit to
adjust to

be accustomed to
be devoted to 
be addicted to
be committed to
be dedicated to

Answer

This is only possible when "to" functions as a preposition, not as part of the infinitive "TO DO."
In your examples, "look forward to" and "an approach to" TO is a preosition and therefore followed by either an object or a gerund.
Hope that helps!

Answer

Let me think for a while. 
I am on my way to doing research into the usage of "to doing."
I admitted to doing this bad thing.
I hope my admission won't lead me to doing more harm than good.

Answer

That's such a great question, so I've just posted an in-depth explanation as a discussion topic:

https://www.italki.com/discussion/164168

Answer

Thank you for answering my questions. I appreciate it