Why all the problems? Perhaps English speakers are put off right away by the very term "imperfect." They might be distrustful: why would anyone want to mess with something that openly admits to not being perfect?
But the word "perfect" in grammar does not mean the same as in common speech ("flawless"). "Perfect" in grammar means that an action has been completed within a certain time frame. And here we have a good clue as to what the function of the imperfect is. The imperfect describes an action in the past where the action was continued or habitual, and where the emphasis is not on the specific time frame but on the fact that the action continued or was habitual. This is why phrases with "used to" or "would" to describe this sort of thing take the imperfect in Italian. Unfortunately, many sentences where you would use the simple past in English will use the imperfect in Italian.
Let's take a look at some sentences, comparing the use of the imperfect and other past tenses.
Dov'eri ieri? Ti ho chiamato tutto il giorno.
Where were you yesterday? I called you all day long.
I know, I know. Why isn't the second part in the imperfect? Because the calling all day is within the specific time frame of yesterday, whereas the person's being somewhere was indefinite. Were they gone all day? In the morning only? For six hours? Not important.
Stavamo mangiando fettuccine ai funghi quando la polizia ha fatto irruzione.
We were eating fettuccini with mushrooms when the police raided us.
Here is a common use of the imperfect: two actions happening at about the same time, with one happening for an indefinite amount of time (imperfect) when another action, at a definite time (passato prossimo here) occurs. Mentre (while) is often used in the clause with the imperfect.
Here's another example of this:
Mentre leggevo The Smiling Eggplant mi e' esploso il computer.
While I was reading The Smiling Eggplant my computer blew up.
Aveva dodici anni quando divenne apprendista di Bellini.
He was twelve when he became Bellini's apprentice.
Here the first phrase uses the imperfect because it speaks of any time during the year the person was twelve. When it was isn't important, the fact that he was a twelve-year-old is important. The other verb is a passato remoto.
Stavo male domenica.
I didn't feel good Sunday.
Yes, this is a specific time frame, but the emphasis is on the continuing state of feeling bad and not so much on the Sunday part.
A very common usage:
Quando vivevo a New York uscivo spesso.
When I lived in New York I went out a lot.
Notice that "used to" is implicit here ("when I used to live in New York I used to go out a lot".)
When "used to" and "would" are used in English to express habits or repeated actions, use the imperfect in Italian.
Cercava sempre di imbrogliarci.
He was always trying to/he would always try to cheat us.
Da ragazza andavo sempre a ballare.
As a girl I used to go dancing all the time.
This usage won't come easily to you right away, but notice from now on when you see or hear the imperfect how and why it is used.