On this topic I can only write about our specific experience of moving to Hamburg.
Hamburg is tough if you are looking for a two person apartment in a good location for a reasonable price.
We were searching and applying for several months but people still told us that we were lucky it didn't take longer than it did.
What do you need?
First of all you will want to prepare a folder of some sort for each apartment you want to "apply" to. This means you'll need a small introduction letter with a photo of you (there are samples on the webs) saying why you want a particular apartment. This is important because the owner of the apartment will make a big part of his decision based on things like if he thinks you can be a trustworthy, reliable, and clean tenant but also if the place even makes sense for you. What I mean is this: We got rejected for an apartment because there was another applicant that works really close to the place and it made more sense for him to have it. We eventually got our place in part because I work right down the street (and because we met the agent at a viewing for another place... and I talked to her for the whole time about how great the apartment is, so nobody even got a chance... sorry!).
Back to the folder.
You will also need to include your last three income statements. The owners will want to see that you have a steady (and high enough) income to pay the rent. They also ask for a copy of your work contract. Another financial thing that's super important is your "Schufa Auskunft"! This is basically your German credit score. (I'll write more about those in another post.) If you haven't been living and working in Germany at all (like my husband) your's will just show up empty so instead of that you'll want to just have a copy of your American credit score (maybe with a little guide of what the numbers mean, because Germans usually aren't familiar with it. We just included that chart that tells you when you are good or "in the green area" ;-) Basically most agents will want you to do financial striptease for them.
If you have all that, packed up neatly in a binder you are good to go and engage in battle.
In Hamburg you will get to an apartment viewing and there will be soooooo many other people/applicants, so bring some time with you! If you want a place don't be shy! Let the agent/owner. Also, it's good to dress nice!! Think of it this way: You're at the Bachelor Show and you want to flirt as hard as you can to be the one he chooses. (Also you will want to ask questions about the place, especially if you have the original tenant present at the viewing.)
If you want the place you ask the agent for a "Selbstauskunft", which is a form you have to fill out and turn in to him. Usually you will give that to him together with your application binder, but in some cases they just want the form. On this form you just fill out stuff about your financial situation and former living situation (so it's good to know the info of the place you rented before). They like to check if you were a good renter at your former place.
And then you have to wait... although it doesn't hurt to check in with them. For the place we ended up renting I called in after our viewing just to let them know that we really, really wanted the place and then again on the day they were gonna make the call to whomever would get it. It's also good to call in even just to know if you need to keep biting your nails or if the place has already gone to someone else. We got rejected a lot before but we learned a lot for the next time.
We did have a few times when we were the ones rejecting an offer to rent. The first time that happened we thought we needed to take the place or we would never find one, but it just didn't feel right. In the end it all worked out and boy am I glad we didn't settle!
Oh! When you look online for places call the agent about when they will have their viewing or send an e-mail with your intro letter!
I think that mostly covers that. Your experience might be very different depending on where you move, but in general these things are good to know before you jump in there.
Good luck!!

