How to find accommodation
First, you need to be realistic about your budget. If you're looking to rent inside the city centre, then you can probably find a one-bedroom apartment at about 400 euros, but you'll need to carefully consider the utility fees; ask to see the utility bills from the previous winter, as the price may increase drastically depending on the season. Outside the city centre, you can probably find cheaper accommodation (around 300 euros for a one-bedroom apartment) but the same caution is advised when it comes to utility fees.
If you speak the Estonian language well enough, you can probably try to rent directly from an owner, through a newspaper posting, through Expat.com's housing section, or through this Facebook page that connects landlords with tenants directly. But if you mostly communicate in English, then real estate websites and agencies are your best bet. You can find a list of real estate websites at the end of this article, as well as a list of trusted estate agencies at the website of the Estonian Association of Real Estate Companies.
What you need to know about the lease
Once you've found an apartment that interests you, it's time to consider the lease -- maybe get a real estate professional to help you understand the details of your lease agreement before signing. Most leases are for at least one year (although it is possible to have a lease for an unspecified term, you can negotiate that with the owner), with a notice period of 30 days, and the deposit is one to three month's worth of rent (usually just one month), which you will get back when you move out. If you rented with the help of a rental agency, be aware that for the first month you'll have to pay a) the rent in advance, b) the deposit and c) the rental agency fee, which in total can amount to three to four times the price of your actual rent.
Utility fees are the big unknown factor here, as usually they're not included in the rent and you have to pay them separately (although they will be mentioned in the lease). The real issue is that the heating bill, for instance, can vary drastically depending on the season, costing you something like 80 euros in spring/summer and 180 in the winter. It is actually not a bad idea to ask the neighbours about things like that when visiting the property.
Useful links
Housing in Estonia
City 24
Kuldne börs
