In advance edit
In many cases, there will be ample warning before a natural disaster actually reaches an area. In such cases, it's best to evacuate before the disaster reaches you rather then when the disaster reaches you. As some warnings for disasters that never strike are inevitable, many in disaster prone regions get complacent, and stop taking warnings seriously. It is important that you at least consider what would need to be done to get out while it is still easy. If authorities tell you to leave in advance, you should listen.
Just in time edit
Sometimes there will be less advance warning, or it will become apparent that staying behind is not a good idea. In these cases evacuation is more difficult, because it's likely that others have also realized a need to evacuate at the same time. Still, even though evacuation can be more difficult, if you need to evacuate, then you need to evacuate. Follow official guidance on what to do if there is any.
While a natural disaster is actively taking place, it may be best to shelter in place instead of evacuating if you are currently in a suitable shelter. Conditions outside are likely dangerous, and even short trips can be perilous. However if your shelter is unsuitable or compromised, evacuation may be necessary to ensure your safety. While the goal of an evacuation before a disaster is to remove yourself from an affected area, that may not be possible or safe while a disaster is ongoing. If removing yourself from the affected area is impossible or unsafe, then the next best thing is to seek a suitable shelter.
Remember, the goal of an evacuation is to get to a safe place. If the place you are at is already safe, it's best to hunker down, even if it's not necessarily as comfortable as you would like.
While sheltering in place may get you through the active disaster, the aftermath may contain unsafe conditions that you should remove yourself from. Following a natural disaster, everyday comforts and even necessities are likely to either be stretched thin or are going to be non-existent. While evacuating following a natural disaster, it is important to be on the lookout for damaged infrastructure, and to give right of way to aid workers and first responders if they are present.
If you require urgent assistance or aid following a disaster, particularly medical aid, food, or water, it is important that you make your needs known to the proper authorities, charitable organizations, or other assisting group. However understand that depending on the circumstances, they may have a limited capability to assist, especially in the area affected by the disaster.