Correct Usage of Used to and Be used to

Knowing the correct usage of "used to" and "be used to" is very important. To start with, let us first know the definition of each term.

Used to followed by the base form of the verb is used to say that someone did something regularly in the past, but no longer doing it at the present time. 

I used to eat candies when I was a teenager.

The sentence tells us that the subject used to eat candies when he was a teenager, but now (that he is not a teenager), he is no longer doing it. 

Be used to, on the other hand, is used to tell that someone is accustomed to doing something. Be used to is followed by a present participle (v-ing).

Sheila is used to singing in public places.

Here, the sentence is trying to tell us that Sheila is accustomed to singing in public places. She does it with ease perhaps. She seems comfortable doing such an activity. Singing in public places is not a strange or difficult situation for her anymore.

Now compare the two sentences.

I used to eat candies when I was a teenager. 

(A habitual action in the past. -Don't say I am used to or used to eating)

Sheila is used to singing in public places. 

(An action someone is comfortable of. Don't say used to sing)

Study this.

I am used to eat candies when I was a teenager.

This sentence can still be correct, but the thought is already different. Here, it seems that the subject is just used by someone to eat candies when he was a teenager.

I am used to eating candies when I was a teenager.

This is absolutely wrong. Be used to + the present participle is just used to convey an action someone is accustomed to until the present time. 

 Be used to (doing) can also mean get used to (doing)

I am used to eating vegetables nowadays.

I get used to eating vegetables nowadays.

They can also be used in this case.

My family is used to cold weather.

My family gets used to cold weather.

My family is accustomed to cold weather.