There have been lots of threads saying "why can't we respec?" and recently some replies saying "you'll be able to soon", so I figured I'd start a thread to explain what it is on the test server.
Basically, on the test server, you go to Mr. Lincoln by Golem Tower and pay 3150 crowns. It says it removes all the cards that you've bought for training points and returns all the training points. Presumably that's the cost per respec; it didn't say anything about further limits on respec frequency.
For comparison, 3150 crowns means that you'd have to pay at least $10 to buy crowns in order to respec. For someone who buys the largest amount of crowns so as for discreteness to not be a big issue, it would be about $4.20 per respec. That's no more than a month's subscription, so for someone who regrets choices made months ago and doesn't want to delete a level 50 character and start over, this should be quite affordable. It's not the sort of thing where someone could respec a few times per day without paying a fortune.
Respeccing in other games is arguably more analogous to rearranging your spelldeck here (which is, of course, free) than to resetting your training points. It shouldn't be necessary to redo your training points more than once in a great while. Of course, for some players, it's already been a great while.
With players unable to get crowns on the test server, it would seem that the respeccing system can't be tested there. That might defeat the purpose of having it on the test server, unless there's some way to get crowns there that I'm unaware of.
I checked with three characters of different levels and it was 3150 crowns for each of them. For a fourth character it was 3850 crowns. Looks like a piecewise formula to me, perhaps based on the level title.