First look for checks, if the checks do not lead to anything, look for other options. Forks, skewers, pins, and maybe even trapping a piece or promotion. Look for circumstances that allow you to be forcing. . For instance a series of checks. Also if I see that I am going to be mated next move, I decide if my checking plan leads to mate or and if not I look for a stalemate
What's your process for solving tactics trainer?

Process? Either I see it or I don't.
I train with other tools and use Tactics Trainer on this site occasionally. I use several other similar tools occasionally.
My process is to review master games and my own games, including blitz (rarely bullet). I study the tactics in actual games. Sometimes these reappear in Tactics Trainer. For example, several weeks after memorizing a particular Paul Morphy game, I encountered a position from that game in Tactics Trainer. The solution went beyond the actual game, but I had invested the time working out everything to checkmate.
Help plz