When I took the taxi, the driver happened to be Tofugu's Koichi.
I ended up getting in an argument with the bus driver.
The driver seemed okay but his car was totaled in the accident.
You know that 運転 has to do with driving, right? And you know that 手 often has to do with a person doing something in words like these. So, a person who does driving is what? A driver.
The reading is all on'yomi, because it's jukugo. You should know the on'yomi reading of 手 by now just by seeing similar word patterns to this one.