Trials is a unique mode. No other PvP can prepare you for it except, to some degree, skirmish. dwit and Forrest (and Telco and oil and red) can agree, it just takes repetition until you pick up the nuances. None of the three of my team are as individually good at PvP as dwit or Forrest, but we had good callouts, knew our strategy before each round's start, etc.
As for how I individually got better, it was just things learned over weeks of ToO ... where to place grenades, when to back out instead of pushing the issue, the difference between rushing on 3v2 and 3v1/2v1, never sticking our heads into sniping lanes if we weren't sniping, how to flank wisely, how to prepare when we could tell they were flanking, etc. We had one above-average sniper and two blade-dancers with shotguns who just split up appropriately to cover the right crossfire areas.
It's just practice, practice, practice. And I know a lot of people hate Thieves' Den, but I actually got to know this one like the back of my hand more than any Trials map except Widows Court. When you can tell your teammates, "I'm rushing the outside heavy with my super" or "They're not outside, they're circling around to our spawn, I'll cover the stairs," or "They're sniping the tunnel, [other shotgunner and I] will take the outside" or "They send one guy around by the outside heavy every time, I'm covering the back lane with an arcbolt," or "they head to the outside left platform to begin each one, spam grenades by the doorway" or on some occasions, "They're taking cover by the doorway, let's rush them -- two on the outside, one in the tunnel," it's crazy how many skilled players you can just outsmart.