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A few really quick comments from my experience and talking to others.
Most people use Loquo to find a place to stay as a sublet in someone else's apartment through the "rooms for rent/shared" link. Make sure you feel comfortable with the people you will be living with and have a good understanding of what you will be paying for monthly rent, utilities and how paying for your first and last months will function since you will most likely only be there for part of the month.
Most places will make you pay for the full month of your last month, but if you move in a little before the first of the next month (like May 2?) then you may be able to negotiate not paying for those last few days since you live are paying for the whole last month. If you are leaving in early August, you might want to look into staying at a hostal for the last few days or staying with a friend since it doesn't make sense to pay 300 Euros for 5 days. You might also decide to save all of your vacation for the last week of work so you don't have to pay for housing the last couple weeks while you travel.
A lot of people look to live in the center of Madrid around Sol or Opera. This often means a smaller apartment at higher prices. My advice is to live somewhere close to where you work so you can walk and don't spend as much time on the Metro. Then, you can take the metro into the center whenever you want and it only takes about 20 minutes and the Nightbuses are great for coming back late at night if you've been out partying.
