The Hebrew greeting, shalom (שלום), meaning "peace" and used for both "hello" and "goodbye" is so well known in English speaking countries that some English dictionaries list it as a Hebrew loan word. Likewise, the ubiquitous English word hi is a commonly used loan word in Hebrew - הי.
So an English speaker would be forgiven for thinking that they have Hebrew greetings taken care of. However, this is not the case. While שלום (shalom) is a widely used and all purpose Hebrew greeting and הי (hi) is commonly used as a casual greeting, they are not the only greeting you will hear or should use when speaking Hebrew. Hebrew speakers are much more likely to use greetings based on the time of day. In the morning, people usually say בקר טוב (bok-her tove) which means "good morning." In the early to mid-afternoon, people usually greet each other with צהרים טובים (tzah-reem tove-em) or "good afternoon." (Note צהרים is usually translated as "noon", but it usually means sometime in the noon to three or four pm range.) In the late afternoon and evening, people use the phrase ערב טוב (air-ev tove.) Late at night people switch to saying לילה טוב (lie-lah tove) or "good night." In English, we often say "good night" to people at any time in the evening if we aren't expecting to see them later – for instance, when leaving the office or after dinner. However, the Hebrew equivalent, לילה טוב, is only used late at night, such as when leaving a late party or going to bed.
Like שלום (shalom), all of these phrases can be used to say either "hello" or "goodbye" depending on the situation. Another option for taking your leave of someone is to say להתראות (la-he-tre-oat.) להתראות (la-he-tre-oat) means "I'll see you later" and is commonly used to say goodbye.
There are a few other greetings you might hear. שבת שלום (sha-bAht shalom), which means "blessed sabbath" is used by Jews around the world as a greeting on the Sabbath (sunset on Friday to sunset on Saturday.) It is also used when taking your leave from people on Fridays before Sabbath starts. On holidays, you will hear people greeting each other with חג שלום (Hah-ge shalom) meaning "peaceful or blessed holiday."
With these greetings, you should be prepared to say "hello" and "goodbye" to any Hebrew speaker you may meet.