1. Explain it simply
一边 + verb 1 + 一边 + verb 2 means 'doing verb 1 while doing verb 2'.
Both actions are done by the same person, at the same time.
2. Show examples
他一边吃饭一边看电视。
Tā yībiān chīfàn yībiān kàn diànshì.
Sandhi:Tā yìbiān chīfàn yìbiān kàn diànshì.
He eats while watching TV.
一边 + verb1 + 一边 + verb2
我一边听音乐一边写作业。
Wǒ yībiān tīng yīnyuè yībiān xiě zuòyè.
Sandhi:Wǒ yìbiān tīng yīnyuè yìbiān xiě zuòyè.
I listen to music while doing homework.
Two ongoing actions, same subject
她一边走一边打电话。
Tā yībiān zǒu yībiān dǎ diànhuà.
Sandhi:Tā yìbiān zǒu yìbiān dǎ diànhuà.
She talks on the phone while walking.
Works with any pair of compatible actions
3. Share a tip
Both verbs need their own 一边 - don't drop the second one, even though English only needs one 'while'.