What is the cheapest hotel in Amsterdam?

Not like dirty nasty cheap. Comfterable, maybe somthing that would be about $400 for a week.

A bicycle with an umbrella.

http://www.hotelsupersite.com/, u have good choices here

There is a big number of Hotels.
Actually, near the Central Station where you would arrive with the train, there is a nice display where you can contact the nicer ones by phone.
Also, there is a local information kiosk called VVV - they can tell you in person which hotels are available within your price range. More important, they will also tell you for most of them if there are rooms available.

An other option is to go to neighbouring towns. Most towns are connected nicely by public transportation, and travel distances are okay.