How are you? = كَيف الحال؟ (kayf al-ḥāl), literally “How is the situation/condition?”

How are you? = كَيف حالُكُم/حالُكَ/حالُكِ؟ (kayf ḥālukum/ḥāluka/ḥāluki), “How is your (formal-plural/masculine/feminine) condition/situation?”

A note on the verb “to be”: Arabic has one (كانَ, kāna), but doesn’t use it in the present tense except in some very rare circumstances. Instead, it is implied or worked around; implied when a definite subject is followed by an indefinite predicate (which can be either nominal or adjectival), worked around when a definite subject is followed by a definite predicate by inserting the appropriate third-person pronoun between them:

هَذا الرَجُلُ مُعَلِّمٌ. (hadhā al-rajulu muʿallimun) = “That man is a teacher.”

هَذا الرَجُلُ هُوَ المُعَلِّمُ. (hadhā al-rajulu huwa al-muʿallimu) = “That man is the teacher.”

Colloquially there are many possibilities and I can only talk about a couple of them. One is the standard كيف حالك؟ but with the colloquial possessive, which is “-ak” or “-ik” (depending on gender), rather than “-ka” or “-ki,” so it sounds like “kayf-ha-lak” rather than “kayf-ha-lu-ka.” Another variant skips “hal” (condition) altogether and just asks “How are you?” or “keefak” (to a male) and “keefik” (to a female). “Kayf” in colloquial can be simplified as “keef.” Another, used primarily in the Khalījī (Gulf) dialect, is ايش لونك؟ (īsh lūnak/lūnik but pronounced “(i)shlo-nak” or “(i)shlo-nach” depending on gender—note the unusual use of a “ch” sound here for the feminine possessive), which literally means “what is your color?”

What’s up? = ما الأمرُ؟ (mā al-amr), literally “what’s the matter?”

What’s new? = ما هِيَ الأخْبارُ؟ (mā hiya al-akhbār), “what’s the news?” (substitute أخْبارُكُم/أخْبارُكَ/أخْبارَكِ akhbārukum/akhbāruka/akhbāruki WITHOUT THE DEFINITE ARTICLE for “what’s your news?”). “Akhbār” is the plural form of khabar, which means “report,” so it’s a bunch of reports, i.e., “the news.”

(A note on plurals: all non-human plural nouns are modified as though they were feminine singular nouns, meaning they take feminine singular form verbs and adjectives and are replaced by feminine singular pronouns.)

A colloquial variant, technically in the Levant (Syria, Jordan, Lebanon, Palestinian Territories) but I heard it used frequently for the brief time I lived in the Gulf, is شو اخبارك؟ (shū akhbārak/akhbārik), meaning “what’s your news?” شو is a Levantine substitute for ما meaning “what.”