How am I supposed to time a run?

Check the Rules. If you need help finding the rules, DM me on Discord. My Discord is in my profile.

From when you start moving to when you complete your goal.

Download LiveSplit and watch a tutorial about it

As people mentioned. LiveSplit and then add AutoSplitter. Yarmi has a good tutorial regarding setting AutoSplitter up.

just press T to get a timer

How do I set the timer on the website itself? I've been timing myself and it doesn't seem right.

When you are in game, press T. That's it.