You get 4 per level, so 80 by the time you hit 20. Then you get destiny points for what is basically epic enhancement trees.
The best way to use enhancements is to figure out (usually before you make a character lol) what your main tree is going to be. For barbarian I usually go all in on frenzied berserker because it's the big DPS. You usually don't want to spend every point unlocking EVERYthing in the tree, but rather work from the top down. You need 5 points to unlock tier 2, 10 for tier 3, 20 for tier 4, and 30 for tier 5.
Sometimes there's a lot of good stuff in each tier, but higher stuff is usually better. So once you spend your 5 pts in the tree (including cores, check the next tier to see if that's better stuff and spend appropriately.
Resetting trees costs a little plat and, as long as you don't reset multiple times a day, is relatively cheap. I usually spend recklessly up until tier 4 or 5, then just reset. Tier 5s also require you to be lv 12 so don't need to worry about them yet. You can also splash into one of the other trees for some low hanging fruit if anything's good, then reset later once you can get something good in FB. Ravager looks like it has some okay-ish stuff in tier 1-2.
Most of the time, by the time I'm 20, I have ~41-45pts spent in my main tree (if you took all 20 levels in a class, the final core requires 40pts spent in the tree), and then depending on my class/build, another 1-3 trees with various amounts of AP spent.
I think my most crazily skewed build was an int-based quarterstaff assassin. It was a super weird build that didn't work great lol. I had half my points in assassin, 11 in inquis for auto-search, ~7 in feydark for perma shield, a ton in harper for int to hit/damage. Like I said, big mess. For a pure/simple build it's easier.