Used to + infinitive or -ing?

There are two forms of 'used to'.

When we talk about past habits and states, especially when they are no longer true, used to is followed by a verb in the infinitive form and 

always refers to the past.

When we want to convey the meaning of 'accustomed to', used to  is followed by a verb in the -ing form; this version exists in all the tenses: present, past and future. In addition it has to be preceded by the verb 'be', 'become' or 'get'.

Past habits and states

I used to have long hair, but no-one believes me!
She used to be so shy, but just look at her now!
Didn't they use to play for Barcelona football club?
My wife never used to like technological gadgets, but now she can't live without them.

Accustomed to

I am used to staying on my own now but I used to be terrified.
After all these years, Jason still hasn't got used to driving on the right.
Don't worry, you'll soon become used to everyone stopping you on the streets to say hello.
It took her a long while, but she eventually became used to eating with chopsticks.

It is worth pointing out here that the 'to' in this 'used to' is a preposition. One way of knowing if it's a preposition is to substitute what comes after it with a noun. If it sounds good, it's correct!

I am used to spicy food. (I am used to eating spicy food)
Jill hasn't got used to her Mac yet; she still misses her old PC.

For the difference between 'would' and 'used to' see:
http://aclil2climb.blogspot.com/2011/09/what-is-difference-between-to-and.html