Finding an apartment or roommates whilst you are overseas is hard to do unless you already have friends here. Even once you are in Beirut it can take some time. It is best to find a place to stay in advance for a few weeks until you find an apartment.
Good places to look for apartments and roommates are: Craigslist Beirut, the Daily Star classified ads, Ahlein.net, EWaseet (Arabic), and the Facebook group: Apartments in Beirut. When you are looking keep in mind that Beirut is a big city and there are only a few areas from which Saifi is easily accessible: Hamra, Achrafiyeh, Borj Hammoud and more recently apartments for short-term rent have become available in Zarif and Sanayeh.
A private furnished apartment ranges between $600-1200 per month for 1-2 bedrooms, and a room in a shared apartment will cost around $300-500 per month. Add around $40/month for electricity, water and garbage, and $20-50 for internet.
In Lebanese culture it is very unusual to live outside of the house until one is married, or to welcome strangers to live with a family, so your roommate is most likely going to be another foreigner.