About one in five skaters will jump and spin clockwise. Despite this meaning that they jump to the right (think about it), this tendency is called "lefty" jumping. It is somewhat, but not entirely, correlated with left-handedness, although there are right-handed skaters who jump lefty (me) and left-handed skaters who jump righty.
First, let me state emphatically that it doesn't matter which way you jump. There is no benefit or deduction for choosing one over the other. It is easier to teach a skater to jump and spin in the same direction, but again, nothing in the rules or in general technique would theoretically prevent a skater from jumping one way and spinning the other. Most highly competitive skaters now have spins in both directions. Ballet dancers have always done multiple rotation jumps in both directions.
Here's a basic guide:
How can you tell which way a skater jumps
If you are a parent, you basically don't need to worry about it. The coach will figure it out. If you're the kind of parent that feels a little smug and happy when your kid is different from everyone else, and you've got a lefty, I give you leave to brag (lefty skaters are cool, everyone knows it).
The easiest way is to just ask them to jump and do a half turn in the air. Most reasonably talented kids can do this on the ice by the time they're working on back crossovers. You can also watch their bunny hops (kicking with the right foot generally, but not always, indicates a righty or counter-clockwise skater; left kick is a clockwise skater,). There are other tests- have the skater face away from you, then give them something. They will automatically turn in their dominant direction. Ask them to spin. Then ask them to spin the other way and inquire as to which one they liked better (they won't always spin right off the bat in the dominant direction, strangely). Have them skate to the exit and step out without stopping. If they lead with their right foot, they're probably righties. Watch to see which foot they lead with going upstairs. Righties will generally lead with the right foot.
Which hand they write with is not the best indicator. A lot of right-handed people skate lefty.
Very young children have sometimes not established a dominant spin direction, or will change. Don't worry about it.
When should you choose
Most coaches will settle in on one direction or the other as soon as the skater starts to jump and spin (around Basic 6/7 or ISI Freestyle 1). But really you can play around with this all the way up to the back scratch or the axel if the skater really doesn't seem to have a strong dominance. I've turned a FS2 skater around; she was fine. I switched in FS3 (see the whole story below).
Can you jump one way, spin the other
This is great, but the way skating is taught in the U.S. a skater will have a much easier time if they spin and jump in the same direction. This is because the basic backscratch spin position is identical to the air position in all jumps. So then you only have to learn it once. However, if the skater and coach are willing to devote the practice time to it, no harm in being able to spin both directions. ISI Freestyle 9 has a reverse axel as an optional element, and FS7 has a reverse jump as a required element. Opposite direction spin in the IJS competitions counts as a feature, and therefore earns points.
Can you do both
What if the first coach gets it wrong
Eventually someone will notice.
What it the class coach gets it wrong
This happens a lot, especially with new coaches who don't know the kids in the program, and with inexperienced coaches. With adults it's not an issue because they'll announce their preference, but children need to be taught to tell the coach that they are reverse/lefty/clockwise jumpers (whatever terminology is in use at your rink.). In particular, coaches who don't know the kids very well will assume incompetence before they manage to get their brain cells lined up and manage to ask the poor child which way they jump. I've seen it happen over and over. Further, if you've got a pretty talented skater who suddenly gets incompetent when the jumps start, gently ask the coach if they've thought about trying the student jumping in the other direction. When I started skating I did not know anything about this. Couldn't jump or spin to save my life. YEARS into training, after laboriously learning to jump and spin counterclockwise, a Patch coach finally noticed that everything was stronger clockwise. He tried me jumping and spinning that way and glorioski.