'The' and 'a'

I wish you’d been there to see the tumbleweeds blow when my teachers asked me the following question……

“How do you know when to use ‘a’ and when to use ‘the’?”

“I’m going to buy a new phone”
“I’m going to buy the new phone”

What’s the difference? Which one is correct? Why?

I really enjoy how this job is making me study my own language. English is in my head and I know when to use certain words but the difficult part is explaining it to a non-native speaker.

Luckily I had no classes today and spent the whole day researching the topic.
By the end of the day the confusion had lifted and I was once again the best ALT ever! : )