The most common way that creatures change their locations in battle is by taking the walk action.
Action: Move action.
Movement: The creature moves up to its speed.
Despite the action’s name, a creature isn’t always literally walking when it takes this action. The walk action can use special movement modes such as climbing, flying, and swimming.
Taking this action is safe only when no enemies are nearby. Walking through the middle of a pitched battle is dangerous, since enemies can make opportunity attacks against a walking creature. The way to move safely when enemies are nearby is to shift or teleport.
Published in Player's Handbook, page(s) 292, Rules Compendium, page(s) 252.