These verbs appear all over in Japanese. Many times, the meaning of a compound verb is simply the combined meaning of the two individual parts. For example, 取り戻す means "take" and "return", or "take back".
If only all compound verbs were that simple... In many other cases, a compound verb takes on a meaning that isn't obvious from the individual parts. 投げ出す（＝投げる＋出す）does not mean to start to throw something—it is closer to "give up" or "quit halfway through."
The best approach to learning Japanese compound verbs is to practice them. Spend just a few minutes every day studying Japanese, and your skill level will advance quickly. Be sure to visit Nihongo-Pro every day, and try a new Japanese quiz, always 100% free.