Well, you apply for a work visa, and your employer sponsors you for it. You have to get your Visa Screen completed with CGFNS, which can take a few months to get the paperwork together and then submitted. Once that's done, its like you're "pre-approved" for a visa. You need to do the obvious things like background checks etc. It took me about a year and a half to get myself ready to move Stateside. However, I dragged my feet for a few months as I was working and travelling around Australia at the time and I was having second thoughts (your typical drama - you meet someone and think you're going to be with them for the rest of your life - thank the LORD that didn't happen!).
It all depends on which country you're from too and the waiting periods for work visa sponsorships for permanent residency. If you're from say, the UK, there is no waiting period. If you're from the Philippines or China, there is a couple years waiting period for your number to come up Its called priority dates and the date that you file for your visa. Its pretty straightforward - go to the USCIS website for more information on priority dates. I'm from the UK, so as soon as I applied, my priority date (date of filing for work visa) was current as there isn't a backlog for my country.
All this being said, once you have done all the paperwork, you become "documentarily qualified" and you just have to wait for them to contact you for an interview at the nearest US embassy. I become document qualified in March this year (2018), about 9 months after I applied. I didn't get my interview until August this year, and then as my visa was approved at the end of the fiscal year, my priority date actually got put back due to so many visa applications. I had to wait until October (this month) for my work visa to be issued. I picked up my work visa 3 days ago. I am now waiting for my agency to book my flights to the USA which should be in a couple of weeks.
Once you arrive in the USA, the border agent looks at your visa and stamps you through and they issue you the forms to apply for your green card. Your work visa permits you to enter the country and work, but you don't get your green card until you apply for it on US soil. Once you fill out the forms they give you, it takes approximately 6 months to get your green card. Thats according to the information that the US government gave me in my work visa package.
In all, its going to take me about 2 years to go from signing the contract with the agency and beginning the application process to getting the green card in my hands. A year and a half to reach America, but 2 years to actually be permanently residing in the United States. I would say that's not too bad. You get a lot done in that time. I could be faster, like I said, if you're pro-active.
If you're already stateside and applying for the green card, I'm not sure what the process is. Since you're still a student, you wouldn't be able to apply for a work visa and get your CGFNS visa screen approved until you had your degree. I'm not sure if they require a Bachelor's or they're okay with ADN, that's something else to look into.
I know that when I was on an F1 visa, I was able to apply for an extension of my F1 Visa for 12 months after I graduated, its called the OPT visa. It lets you work and gain experience in the USA in the field you trained for. I got offered a job at the hospital that I precepted at, and it came at no extra cost to the hospital and I was there for a year. It's a good opening. I would recommend you apply for the OPT visa once you come to the end of your program, and then speak to hospitals that might be willing to sponsor you.
Good luck, I hope this helps!