I just transitioned in May / June of this year and I am intimately familiar with this process. I will try to PM you in the next few days with more detail, but I will give you the short version now (some is a repeat of the above posts):
1. Write your resume (actually, write a base resume that you will use to write company specific resumes off of)
2. Send your resume to as many reviewers as possible. If you are using Bradley-Morris as a headhunter they have a resume review that is part of their service (not plugging them, just passing along info). Compile and use the feedback they give you. If you are really really lucky someone on here might offer to review your resume for civilian nuke specifics.
3. Sign up and register your resume on all of the utility websites. Some jobs may only be open for 1-2 days, and if your resume is already on file, it makes it much easier to apply
4. Scour utility websites daily, and sign up for e-mail alerts.
5. Be prepared to pay for your own flights for initial interviews, most companies will only pay to fly you out for 2nd / final interviews
6. Practice for the POSS test (do a search, there are some books that can help, mostly practice ASVAB's)
7. Practice STAR interviews, preferably with several people, but even if it's just one person it makes a big difference
8. Take any interview that's offered, and remember that ANY contact by ANYONE in the company is an interview
9. Take notes during interviews, especially peoples names. Send thank you notes to everyone you have contact with at the company, from the interviewers to the lady that offers you a cup of coffee.
That's just the highlights off the top of my head, hope it helps