I just arrived in Cologne 6weeks ago and it took me 2weeks to find a flat. I found it quite hard as lots of students were looking for somewhere at that time so maybe now it will be easier. I used
www.wg-gesucht.de which is where I found the place I am staying in now. All the flats advertised are Provisionsfrei (without extra charges) and there is the option to search for Zwischenmiete (particular period of stay), single apartments or WGs (Wohngemeinschaft, sharing a flat with other people). Although the website is mainly advertised for students, it is also for non-students. They have a lot of one bedroom apartments appearing everyday.
If you are planning to get a flat before you arrive your best bet would probably be to go for a zwischenmiete, as people are unexpectantly going somewhere for a short time and need to find someone quickly. If i were you, I would do that and then find something more permanent once you arrive as it can be quite hard to find somewhere if you are not there in person.
I also used
www.studenten-wg.de which has WGs only for students, but one bedroom apartments for anybody to rent.
I hope that helps, good luck with the search!