The idiomatic phrase used to (not use to) has two senses: (1) an adjective meaning accustomed, and (2) an auxiliary verb meaning, roughly, did and implying that an action was habitual in the past and does not continue in the present.
Examples
In the context of used to, used may mean accustomed—for example:
The show’s amazing costumers, who are used to doing things on the fly, make the necessary adjustments to our outfits while we do a music check. [People]
But Japanese bosses are not used to judging people by their performance . . . [Economist]
Used to may be used as an auxiliary verb—similar to did—used to indicate that a state, habit, or action took place in the past and does not continue—for example:
Hall of Famer Billy Williams said they used to have a TV in the clubhouse when he played, but it was a little smaller. [MLB.com]
Bridgwater Carnival used to be staged on the Thursday closest to 5 November but moved to a Friday in 2001. [BBC News]
Used to vs. use to
Used to is often written use to—for example:
We use to go to the beach every summer.
This happens especially often with the phrase get used to it, which some write as get use to it.
Didn’t use to vs. didn’t used to
Some grammarians argue that the negative of used to should be didn’t use to. The logic is that didn’t supplies the past tense and hence use should be in the present, just as in the phrase I did go, did supplies the past tense and go stays in the present tense. But because the idiom used to derives from an archaic sense of used preserved only in this idiom, used to loses its meaning if its form is changed.
The best way around this problem is to avoid both didn’t used to and didn’t use to. If you must employ used to negatively, consider going with never used to. But used to is an idiom, so we don’t have to use it in grammatically unquestionable ways. In informal contexts, there’s no reason to fuss over it too much.
