BE AGGRESSIVE!
No matter how good you think you are, the ideal private job will not arrive on a silver platter. From day one of your residency aggressively collect information about private groups in your area of interest. Obviously it helps if you are doing residency where you want to eventually work. If not, the ARRO directory is your friend. Get to know residents in your area of interest and they can help you.
If you can, get involved in ARRO as it will help you make connections up the wazoo.
Starting mid PGY-4 or so, start sending out feelers to private groups. Depending on the group and how well you know them (ie. former residents) you can email your CV and cover letter or talk to them directly on the phone.
Be discreet! If you've done all the hard footwork making contacts don't just give them away to other residents.
I personally do not find head hunters useful, but I'm not shy about giving them my info as you never know if they can give you a sweet lead.
Post your CV on the ASTRO website early and look for new job openings frequently.
A final bit of advice: many of the best private jobs are not publicly advertised. This is why contacts are so important.
In my case, since I post under one identifiable username (ie. not radoncanon) I have personally made numerous contacts from this forum alone. Many current and former users have been a tremendous help in landing a residency spot as well as the current job search.