A popular option for those who have spent at least three years in Spain in full-time education is to make an application to convert their visa for the purposes of study to one that enables them to reside and work here.
There are effectively two options – to live here and accept an offer of employment or to live here and set-up your own business. The initial visa granted has a duration of one year, renewable.
An interesting alternative, for those who have completed a high level of studies (Masters/PHD level) would be to apply for a one-year visa to search for employment. You will need medical insurance and proof of your ability to support yourself economically for the duration of the visa.
While you are not permitted to work with this type of visa, upon finding suitable work, you may convert the visa to a residency and work visa (as mentioned above).