Personally, I can't really tell you how I know... but eventually you'll develop an eye for it, especially if you own females. I'll try to explain...
In general, traditional plakat girls are larger and have more plain fins than the others. Compared to veil tail girls, their fins are a lot more trim, but they're still rounded to some degree. there's none of the droopy cauldal, and the anal isn't quite as long. They have 2 rays.
Veiltails also have 2 rays, but their tails and anals are longer, with that droopy/swoopy look to them. Their anal rays start short but progress to long towards the tail, and their center caudal fin rays tend to be longest.
halfmoon plakat girls are supposed to have super trim fins, with very even anal fin rays. Their short cauldal fins have sharper more defined edges. They have at least 4 rays.
Halfmoon girls have longer fins (at least 4 rays as well), sort of like a longer version of the hmpk girls. The anal fin rays stay pretty uniform in lenghth. Their caudal fins also ahve the sharp defined edges without the curve.
crowntails are pretty easy to identify XD
I hope I didn't confuse you! I'll see if I can find several pictures and use colorful lines to show you what I mean.