used to

We use used to + infinitive to talk about a past situation that is no longer true. It tells us that there was a repeated action or state in the past which has now changed.

She used to be a long-distance runner when she was younger.
I didn't use to sleep very well, but then I started doing yoga and it really helps.
Did you use to come here as a child?

be used to and get used to

Be used to means 'be familiar with' or 'be accustomed to'.

She's used to the city now and doesn't get lost any more.
He wasn't used to walking so much and his legs hurt after the hike.
I'm a teacher so I'm used to speaking in public.

We use get used to to talk about the process of becoming familiar with something.  

I'm finding this new job hard but I'm sure I'll get used to it soon.
It took my mother years to get used to living in London after moving from Pakistan.
I'm getting used to the noise now. I found it really stressful when I first moved in.

Be used to and get used to are followed by a noun, pronoun or the -ing form of a verb, and can be used about the past, present or future.