1. Explain it simply
State what happened first, then use 于是 to give the action or result that naturally followed.
Order: Clause A，于是 Clause B. 于是 opens the second, follow-up clause.
于是 expresses consequence in time - 'and so, thereupon' - not a strict logical cause like 因为.
Keep 于是 at the head of the second clause, not at the very front and not inside the first clause.
2. Show examples
外面下雨了，于是我们没有出去。
Wàimiàn xià yǔ le, yúshì wǒmen méiyǒu chūqù.
It was raining outside, so we did not go out.
the second event follows the first
天太热了，于是我打开了空调。
Tiān tài rè le, yúshì wǒ dǎkāi le kōngtiáo.
It was too hot, so I turned on the air conditioner.
于是 gives the next step
我们迟到了，于是老师很生气。
Wǒmen chídào le, yúshì lǎoshī hěn shēngqì.
We were late, so the teacher was angry.
于是 heads the result clause
3. Share a tip
Use 于是 for what happened next in time; for a strict reason, reach for 因为...所以 instead.