Each horse is different, and there are many factors that go into deciding what age to start them hunting. I have started one hilltopping at 3.5, and she went first field the next season. Others we have had usually start at 4-6 (I do not typically spend an entire season hilltopping them like some others do). Things I consider before hunting them are: if they physically and mentally mature enough yet, if they are well-enough broke under saddle, if they know how to jump, if have a brain (goes to maturity), if they have spent a good bit of time going x-country from home, as well as being trailered various places, and behaved, if they trailer well, if they can handle being in company, etc.
During the summer, we spend a lot of time hacking on the weekends taking the greenie out with an old campaigner (and/or a small group), where they learn how to cross water, get gates, stand and wait, and start jumping coops/walls (depending on how old they are). Our hunt does small Monday evening walking-only trail rides, which is good to get them started, and then we have big Saturday morning rides in August.
The best "training" for a potential hunt horse is to do exactly what you would do out hunting, sans hounds (but getting a group of dogs to go hacking with you helps!).
Homebred thoroughbreds, forward/mature, I start "hunting" (toddling at the back of the field with a trusted buddy, short hunt days, real quiet) at 2 3/4 (late fall of 2 yo year) or 3 1/4 (spring of 3 yo year.) Off track tb's, ditto. Less mature horses (homebred tb who was notoriously slow to come around) toddling at 3 3/4, hunting properly at 4 3/4.
Normal breaking/training exercises, regular conditioning, lots of trail riding - start short with just 1 or 2 barn buddies, buildign to longer, building to more peeps, buildign to shipping/riding, building to hunt rides, building to hound walking.
Making a proper field hunter is PROGRESSIVE. As some have said, some horses are just good, no matter where they came from, with little to no systematic progressive training. Others take months/years. Others never get it.
But increase your odds by doing the small steps progressive training systematic thing.