What are my options to study and as a student in Spain?
If you are already a student in Spain and you wish you work, you need to apply for an authorization to work while you are a student.
What are the options that exist for those who have already finished their studies?
If you have already finished your studies in Spain, there is a type of residency that you could apply that will allow you to look for job for a year. On the other hand, if you have graduated in your country of origin, there is a residency that you coluld apply to to come do an internship in Spain. (Prácticas Laborales).
Do you want to work while you are studying in Spain? More Info
Residency to look for a job More Info
Residency to do an internship (prácticas) More Info