A quick way to say “good morning” is zǎo (早), which literally means “early.”
A fuller expression is zǎoshang hǎo (早上好), which literally translates to “good morning.” Zǎoshang (早上) means “morning,” while hǎo (好) means “good.”
You can also say 早安 (zǎo ān). The 安 means peaceful, so you are essentially wishing that the other person has a peaceful morning.
In China (at least in Beijing, where I live), 早 (zǎo) by itself is probably most common, followed by 早安 (zǎo ān). It is more rare that people will say 早上好 (zǎoshang hǎo), but all three are correct. If you are addressing someone, you usually say their name or title first. For example, 老师早 (lǎoshī zǎo), which means teacher (老师 (lǎoshī)) good morning.