Start here:

https://www.speedrun.com/terraria/guides

If you have questions, ask in the Terraria forum.

their discord is also great

I completed a speed run and saw time and game time while filling out the details. I filled in-game time but didn't know what to do with time. What do I do what that?

The mods should, hopefully, retime your run themselves. For now, put an estimate of your real time (RTA)