While all the advice here is excellent, I suspect your issue is a simple one of endurance. Trotting in the beginning CAN feel like running up a flight of stairs. This is part endurance and part you're learning (it feels like this because you're using your thighs too much over your core, but it takes TIME to figure this out). You WILL learn the mechanics and feel better and it WILL stop feeling like a stair race. But it can be VERY challenging initially (ask me how I know) ;)
If you have the freedom to practice on your own, I highly recommend after a warm up (at the walk) you move to trotting the straight (long) sides of the arena, doing walk transitions for the corners/short sides. (This is also excellent transition practice!) Do a few laps like that in both directions, then try a full circuit at the trot followed by a break, then maybe lap/cross diagonal/lap if you're up to it. Don't worry about form other than you're not flopping all over/whacking the saddle. At this stage your goal is getting strong enough to learn effectively.
Give yourself lots of mini breaks to start and you'll find you will build your strength very quickly (and can then focus on the finer points, diagonals and posting *correctly*, etc)
And most important - HAVE FUN!