To Hand Over
To Ferry Something Across, To Lay Something Across
transitive verb, godan verb
Because the hiragana ends with an う sound, you know this word is a verb. The kanji itself means transit. It's also in the verb 渡る, which means "to cross." But with 渡す, it's more like you're sending something across instead, usually to another person. So 渡す means to hand over.
It can also mean to ferry something across a river, or to lay something across an expanse, like when you lay a plank over a pothole or build a bridge across a river.
To remember the す in 渡す, think of suing someone. When you sue (す) them, you have to hand over the papers to let them know you're suing. If you don't 渡す the papers, you can't sue!
The reading is the same as the one you learned with the kanji.
彼が私にペンを渡してくれた時、胸がどきどきした。
When he handed me the pen my heart was pounding.
上司に辞表を渡す時、手が震えました。
When I handed in my resignation to the boss, my hands were shaking.
渡された番号に電話を掛けてみたが、つながらなかった。
I dialed the number that she had given me, but I couldn't reach her.