When applying for a flat (usually only relevant for WG's or normal flats), you will be required to provide the landlord with various documents. Usually this includes a fully filled out "Mieterselbstauskunft" form (application form) which will be provided by the landlord, proof of your financial status (or of your parents' financial status), proof of your enrolment and/or job contract and some may ask for your SCHUFA report (credit rating).
Landlords usually require a security deposit of three months' rent before you move in. This security deposit will be returned back to you once you move out of the flat, providing you keep your room or flat in good condition.
Please be aware that there are some fraudulent offers on the internet. Signs for this are bad German or English and cheap prices for huge flats or flats in the most wanted areas. Often these people will mention how they have moved abroad and therefore cannot meet you in person. Anyone who asks you to send them money before you have even seen the flat in person, should be immediately ignored. If you are not sure whether someone is a fraud or not, always ask for a second opinion.
Registering your address in Germany
Once you have found accommodation and signed the contract, you need to go to the Bürgeramt (resident’s registration office) within 2 weeks and register yourself at your new address. This is compulsory in Germany and if you don't or do it late, you will be charged a fee.
The Rundfunkbeitrag is a tax for public-service broadcasting paid by everyone living in Germany. This tax is separate from the rent and is paid directly to the ARD/ZDF/Deutschlandfunk Rundfunk. It currently costs 17,50€/month and is shared by all tenants of a flat. If you live in a WG, the individual contribution will be split between the people living in the flat. You will be contacted directly by ARD/ZDF via mail once you have moved in.
As most accommodation in Frankfurt is not furnished, you will need to buy your own furniture. You can either buy new from shops such as IKEA or you can look for cheap or even free used furniture. The best places to find furniture are the Frankfurt flea market on the Schaumainkai and Osthafen, in second-hand furniture shops such as Neufundland (www.neufundland-frankfurt.de), online in private ads on websites (https://www.ebay-kleinanzeigen.de/) or on Facebook (free your stuff group Frankfurt).
Sometimes, when you move out of a flat, you may be required to repaint the flat before getting your deposit back. Make sure you ask in advance what the landlord expects and whether the previous tenant has actually painted the walls or if the landlord will be taking care of this.
Good luck with your search!