"My father is a taxi driver."
しゅ (written in kanji as 手, meaning "hand") is added to certain nouns to indicate someone who does that (the thing the noun describes). Hence うんてん (運転) "driving/operating (machinery)" --> うんてんしゅ (運転手) "driver".
Also happens in compound words such as せんしゅ (選手), meaning "player" (of a sport).
For finding the on'yomi and kun'yomi pronunciations, I would personally suggest going to Wiktionary and typing the kanji into the definition. Or you could look at this link here (https://en.wikipedia.org/wiki/Ky%C5%8Diku_kanji) and learn the meanings and pronunciations of several kanji.