Research assistantships are primarily found in graduate school at the level of the master's degree or the doctoral degree. These positions are very competitive. Many provide a generous stipend and some subsidise tuition costs as well. Assistantships are granted at the department level, which is where your search should begin. If you are already in graduate school, then you should talk with the Chair of your department about assistantship opportunities. Some research assistantships are advertised nationwide and some are advertised within the department only.
Think about graduate school long before you graduate with your bachelor's degree. Participate in campus activities that will enhance your resume when applying to graduate school. For example, if you are interested in veterinary medicine, seek out opportunities to help professors at your current university. Investigate internships with the local humane society or a local veterinarians office.
Write a compelling personal statement for your graduate school application. Statements are generally between 700 and 900 words and give admissions personnel an opportunity to get to know you better. Some tips on writing the personal statement: Focus on what is unique about you. Write in the active voice (subject and verb should be close together without unnecessary prepositional phrases). Write a compelling first paragraph (here is where you can hook the reader). Avoid references to high school experiences or controversial topics. * Write about research areas you are interested in pursuing and why.
Research schools that have professors doing research in the field in which you are interested. Web profiles of professors will often allude to their research interests. Find a professor who is doing research in your field and contact her about opportunities at that particular university.
Make note of deadlines. All universities and departments have application deadlines. You may need to take graduate admissions exams such as the GRE, GMAT or MAT in order to apply. These exams may only be offered a few times a year in your area. You will need your scores when you apply, so plan accordingly.
Apply to at least six schools. Graduate school is competitive. Consider the geographic area you are applying to in terms of cost of living, travelling back home and opportunities for growth in your discipline.
If you are not sure what you are interested in researching, there are also teaching assistantships available at most universities.