1. Explain it simply
差点儿 means 'almost, nearly'. It marks an event that came close to happening but did not.
Word order: Subject + 差点儿 + verb phrase. Most often the event is something bad you were glad to avoid.
差点儿 + verb (no 没有): the event did NOT happen - 我差点儿迟到了 means I was almost late, but I wasn't.
With an unwanted result, 差点儿没有 + verb often still means it almost did not happen - 差点儿没有及格 means almost failed, but passed.
2. Show examples
早上太急了，我差点儿把手机忘在家里。
Zǎoshang tài jí le, wǒ chàdiǎnr bǎ shǒujī wàng zài jiā lǐ.
This morning I was in such a rush I almost left my phone at home.
almost left it behind, but didn't
我差点儿迟到了。
Wǒ chàdiǎnr chídào le.
I almost was late.
差点儿 + verb: almost, but not late
这次考试我差点儿没有及格。
Zhè cì kǎoshì wǒ chàdiǎnr méiyǒu jígé.
I almost didn't pass this exam.
差点儿没有: almost failed, but passed
3. Share a tip
差点儿 comes before the verb, never at the end - say 我差点儿迟到了, not 我迟到了差点儿。