If an activated ability of a creature you control costs no generic mana to activate (for example, if it costs , it costs, or it costs only nonmana actions such asor "Sacrifice a creature"), Training Grounds simply won't affect it
Each one gives your commander a bonus that will help them (and therefore help you) in the game
One of my favorite cards in the deck, for example, is Workshop Elders, which gives artifact creatures you control flying
But in addition to that, you can also cast it for its dash cost, basically ensuring you can trigger any possible ETB effects you have each turn
There are very few cards currently in Lorcana that interact with your opponents lore count, but the majority are in ruby