Hi sara, welcome to the board.
The accommodation finding topic has been discussed in depth on this forum, please do some
SEARCHES
You will find that if you do your research, you will get results. You get out of it what you put into it
I will add that if you want your
OWN APT. in the center of Madrid (or outside of Madrid for that matter), 350 Euros/month is an impossible budget. As you will read on many accommodations threads here, 350� will get you a room in a shared flat with 1-3 other people.
Your own studio in central Madrid will be at least 550 Euros/month and a 1 bedroom will be about 600 or 650.
Saludos,
jer...