The Arabic word for “compass” is بوصلة (būṣlah or bauṣalah). It is a loanword, imported from the Italian bussola. “Points” is نِقاط (niqāṭ), singular نُقطة (nuqṭah). Here are the main directions (اتجاه ittijāh, plural اتجاهات ittijāhāt) on the compass, please note that they usually take the definite article:

• north: الشمال (al-shamāl or al-shimāl)
• south: الجَنوب (al-janūb)
• east: الشَرق (al-sharq)
• west: الغَرب (al-gharb)
  

These can be combined to form the derivative compass points:

• northeast: الشمال الشَرقي (al-shamāl al-sharqī)
• northwest: الشمال الغَربي (al-shamāl al-gharbī)
• southwest: الجَنوب الغَربي (al-janūb al-gharbī)
• southeast: الجَنوب الشَرقي (al-janūb al-sharqī)

The words شرق and غرب have to do with the rising and setting of the sun, respectively, and غرب has the additional, related, meaning of “going away” or “departing,” from which is derived the word غَريب (gharīb), which means “strange” or “alien” or “foreign.” I guess there’s a joke in there about strange westerners. The words شمال and جنوب, meanwhile, both derive from terms for “side” or “flank” (شمال can mean “left” although I’m pretty sure that’s an archaic meaning); also, the Arabic word for “right,” يَمين (yamīn) comes from a root that can also (if somewhat archaically) mean “south” (from which we get the name of the country of Yemen, which is in the southern part of the Arabian peninsula). I think, but don’t quote me on it, that this reflects the fact that east used to hold the “top” position among the cardinal directions, presumably due to the whole rising sun thing, which would put north on the “left” and south on the “right.” That’s not just true for Arabs; medieval European “T-O” maps often had Asia (to the east) at the top, with Jerusalem as the focal point.

FYI, since it’s relevant to our topic and our language, in Arabic “the Middle East” is الشرق الأوسط (al-sharq al-awsaṭ).