Here's my unsolicited advice. I went through this process just over a year ago. I am by no means an expert and what I write here may or may not be consistent with your experience.
My advice is to start early and to keep searching for opportunities until you accept an offer. What does early mean? For academics I would contact your top choices in June. Send them an email with a short (few sentences) message stating why you are interested in them and attach a detailed cover letter describing your experiences, vision, and goals plus your CV. If you are applying to academics and private practice make sure you tailor your cover letter accordingly. Have your chair/advisor read your cover letter before sending it out. Having a solid cover letter is key.
You likely will get mixed responses. Hopefully, some will be positive. Expect to hear nothing from about a 1/4 to a 1/2 of the programs, at least initially (this does not mean you are out of the running). A few departments will offer interviews before ASTRO. For academics, I'd say most go on 2 or 3 before ASTRO but if you go on none this does not mean you will not find a job.
As ASTRO approaches (1-2 months before) you should monitor the ASTRO career center website closely. If a job is posted and you are even a small bit interested apply for it. This is also a good time to reconnect with programs you contacted back in June if you had not heard back from them for awhile. During ASTRO expect to spend most of the meeting interviewing. This round is a screening process and everyone does it differently. It may involve meeting with a junior faculty for coffee, having lunch with a chair, I heard of one person who met with a therapist for 10 minutes and no one else. Some departments will have you meet with multiple people during multiple days in offsite locations. This can be very time consuming. You also will have a few interviews in the career center which is a strange experience. Plan to be at ASTRO from Sunday morning to Wednesday night.
After ASTRO the programs most interested in you will invite you for a formal interview. I'd say most departments interview 4-8 people per slot (from my experience). I'd continue to monitor the career center website, careermd.com, etc during this time as good opportunities open up after ASTRO. The great thing about these interviews is that the programs cover all of your expenses and they take you out for a nice dinner. During these interviews you will meet most of the faculty in the department and often faculty in med onc and surgery. It is a good idea to prepare yourself for each interview. Read up on everyone beforehand, check them out in pubmed, have questions ready. Most places will also have you give a presentation, typically this will be on your research and lasts 30-60 minutes. Be prepared to answer questions afterwards. I used the exact same presentation everywhere I went regardless of the position. The presentation is very important, practice ahead of time. A good idea is to give it to your home department and get feedback. Know your audience, speak confidently, and show enthusiasm.
Typically, there will be a second round of formal interviews. Usually, these are offered to 1-3 people per position. So if you get this far you are doing great but still may not get an offer. The second round often includes a tour of the area with a real estate agent. A presentation is not required for this round. You will likely interview with a new group of people, many in other specialties.
It is important to realize there is no set timeline here. Unlike the match, an offer can come at any time. I know people who signed offers during the summer and others who did not sign until March. The key is to not get discouraged and to keep pushing ahead and keep looking for opportunities. Once you get an offer most programs will want a decision within a couple weeks (maybe sooner). You may get an offer very early at a place which is lower on your wish list. This can make for a difficult decision, especially if you are risk adverse.
If you are set on academics be prepared to go to any part of the country. The number of academic jobs is limited and if you are set on staying in a certain region of the country there may not be a good job available the year you apply. Be flexible and apply broadly. Keep your chair/advisors informed of where you interview and where you are most interested. During your interviews the most important thing is to show enthusiasm and be able to clearly describe why you want to be there and what you plan to accomplish. Don't take anything personal and remember that any rad onc job is a great job.
If you are looking at private practice much of what I wrote may not apply to your situation. Private practices tend to move quickly and obviously care less about your research/academic accomplishments and more about the "three A's". If you are applying to both or on paper look academically oriented be prepared to address these issues in your cover letter and during your interview.