General question: How does one look for a place to rent in Amman?

I'd recommend http://www.expatriates.com/classifieds/amm, check "Housing Available".

Many thanks, RoyalDuke. My question was more general one, i.e. I wanted to know how do expacts typically look for apartments/villas?

Most of the people wonder around to check out the area and if the apartment is available by asking the "haris" (landlord or the guard).
If you don't have time you can contact a real estate agent.

You're welcome. What Primadonna works, but like she mentioned, it takes time to do so. Better is through local contacts from work or people you meet socially, so you pay no fee to an agent.

Usually through real estate agents or websites for expats such as this one!
(Moderated: please post in the housing section)