I disagree with the previous posters. NOW would be a good time to start applying. If you wait until after you graduate, all the new grad positions will be gone. I started applying for jobs in January of my senior year of college. I interviewed and had a job offer in March, graduated in May, and started working in September (by choice).
You cannot sign up for NCLEX until after you've already graduated, mainly because you are not eligible to take NCLEX until you have completed your program. After you graduate, your school will send your transcript along with your application for the test and for licensure to Pearson Vue. You will then receive an Authorization to Test (ATT), and you will be able to schedule the test.