Check the local paper's classified ad section under rentals. Look in the Socorro Phone Book's yellow pages under Apartments 5. Find someone who is looking for another roommate. So be prepared to have this cash available. When you finally move out you will not pay the last months rent and you should get back your security deposit as soon as the landlord has checked the place for damages.
Most apartment complexes have a laundry facility.
If you do not have access to laundry facilities at the place you choose to live then you can use one of the public laundromats. One is located on California Street near the Lota-Burger.