"registered nurse" and "training"?

what kind of training does a registered nurse need to go through shortly after she becomes an RN? What about any training 1 Yr. after being an RN? What training must be done in order to become a Nursing Supervisor?

Depends on what type of nursing you want to do.
If you go to a med-surg floor after graduation, you should expect a 4-10 week orientation (depending on your skills, experience, and the hospital and their need).
If you go to a specialized unit (ER, ICU, NICU, L&D), expect a longer orientation. You're not only new to plain ol' nursing, but you're new to that speciality.

Read world nursing (different than what's learning in nursing school)- A year out of school you'll be doing a LOT. Depending on what floor you're on, how short staffed they are, and how good you are-- you could be in charge. No in charge of the whole floor, but functioning as a charge nurse or team leader. You might be expected to orient new grads (while you're thinking "But I'm still the new grad, aren't I?")
For nsg mgt- if that's what you really want to do. After you graduate, go right back into school. Chances are, where you work will pay for part or maybe all of your school. Do your BSN or MSN. Work a lot, get your experience, and show you're willing to go the extra mile. Get on board, volunteer for extra projects and come in when they're dying for help. It will help you get into the mgt position you want. Most of the time they want someone with a MSN. But you can get in with a BSN, and maybe even an associates degree with experience and intention to get a BSN.
HTH.

some hospitals hve a graduate entry scheme, where nurses can apply straight out of college/unis

generally speaking, depending on whihc dept you want to become a superviser in, you need to complete a post graduate certificate in that area. then usually but not always), you need to complete a masters in nursing (1 yr)...

to complete a masters you need at least 3 yrs full time work under you belt.