If you are serious about finding the right apartment, you need to invest quite a lot of time, use all sources available, and most importantly, stay motivated.
Jot down some areas of first, second, and third choice, get your list of minimum requirements ready and start visiting properties.
Given the lack of rented housing, a lot of the best places are not advertised, but are recommended by word of mouth because landlords prefer 'known' tenants. Talk to friends, family members, classmates, work colleagues, etc. and let them know that you are looking for a place to live. The more people that know you are looking, the higher the chance you will be pointed in the right direction.
Most of the rental properties are published on online property portals. One of the biggest online property portal in the Netherlands is Funda.nl . Huurwoningen means homes for rent.
There are also housing mailing lists. When you register you get ads that are not advertised mailed to your inbox. This is very easy, and usually you can find good value housing. For a Yahoo mailing list for Amsterdam go to http://groups.yahoo.com/group/amsterdam-housing .
You can also have a look on several Facebook housing groups. Search on keyword terms like housing, short term rental or woning te huur. For a housing group in Amsterdam go to https://www.facebook.com/groups/1480904505525292
What? Yes! Supermarkets have bulletin boards and at times people will place rental ads on the board. The advantage of supermarket bulletin boards is that the property on offer is always in the local area. Thus you can pick your areas, go to the local supermarkets and visit the properties all on the same day. Universities and libraries have similar notice boards, the advantage of these is that they are targeted at students and therefore most probably cheaper than most other rental properties you will come across.
A good way of searching for housing in the Netherlands is through classifieds advert portals. Look in local newspapers, especially the Wednesday edition of Telegraaf. You will find different offers, but probably few will meet your needs, so be quick - as the good ones go fast. Also, with the classifieds, you need to be careful. There have been many stories of people giving money and never receiving a key, nor ever seeing the so-called landlord again. Or worse, having received a key, they move in, only to find other people already living there. As a rule, never pay more than 3 months rent in advance, 1 for rent, 1 for the deposit, and one more if it is a furnished apartment. Preferably deposit the money on the landlord's bank account, and never give them cash.