How do I record a workout on my Apple Watch?

Start the session on the watch and log sets from your wrist, with your coach's cues on screen.

Install the watch app
It comes with the iPhone app. If it is not on your watch, install it from the Watch app on your phone.
Open Colossus on the watch and start the session
Today's assigned session is there. Cardio and strength both start from the watch.
Log from the wrist
Each set shows the target and your coach's cue. Log it as you finish, and the rest timer starts itself.
Keep the app in the foreground while recording
This is the one that catches people out. There is a guide in the app explaining exactly what to do, because a session that ends up in the background can lose data.

Worth knowing

Heart rate and calories are read from the watch during the session.
The session syncs back to your phone when they are next together. You do not have to end it on the phone.