The hour and minute hands are simply a push-fit on the concentric spindles that turn them.

Grip the minute hand either side of the spindle, between your thumbnail and a fingernail, and pull it off.

In the same way, remove the hour hand.

When you come to replacing the hands you can simply push them back on, the hour hand first. Make sure they are both accurately aligned on the 12 so that the hour hand will point directly to an hour every time the minute hand passes 12.