In the Czech Republic there are estate agencies, which will help you to find a flat to rent or to purchase. For a flat purchase, estate agencies usually do not require a fee (or rather, they require it from the seller). However, when arranging renting, estate agencies demand either a payment in the form of a fixed sum for mediation or at the amount of one agreed rental payment, or possible a 2-3 multiple of the monthly rent.
You should be aware of some Czech expressions in case you want to buy or rent an apartment in the Czech Republic. There are different sizes of flats: 3+1, 2+1, 1+1 etc. The first number always means number of rooms (without toilet and bathroom), the second is kitchen. Sometimes you can see 1+0. This is one room flat with kitchen included.
If you want to find your apartment without estate agency use this website: http://www.bezrealitky.cz/
Renting a flat in bigger city is always quite expensive. You should choose the location very carefully because the prices differ. You can find the cheapest apartments in block of flats in the suburbs but you have to count with worse traffic accessibility.
Update: NICM, 02/2014