If you are organising a major public event, you will clearly need a robust and detailed approach to planning as well as professional involvement. If you are holding a local firework display, such as those organised by many sports clubs, schools or parish councils, you still need to plan responsibly, but the same level of detail is not necessary or expected.

Before the event:
Think about who will operate the display. There is no reason why you should not light a display yourselves provided it only contains fireworks in categories 1, 2 and 3 but catergory 4 fireworks may only be used by professional firework display operators.
Consider whether the site is suitable and large enough for your display, including a bonfire if you are having one. Is there space for the fireworks to land well away from spectators? Remember to check in daylight for overhead power lines and other obstructions. What is the direction of the prevailing wind? What would happen if it changed?
Think about what you would do if things go wrong. Make sure there is someone who will be responsible for calling the emergency services. Make sure you obtain the fireworks from a reputable supplier. If the display is to be provided by a professional firework display operator make sure that you are clear on who does what especially in the event of an emergency. Ensure you have a suitable place to store the fireworks. Your firework supplier or local authority should be able to advise. If you plan on selling alcohol the bar should be well away from the display site.

On the day of the event:
Recheck the site, weather conditions and wind direction. Don't let anyone into the zone where the fireworks will fall or let anyone other than the display operator or firing team into the firing zone or the safety zone around it. Never attempt to relight fireworks. Keep well clear of fireworks that have failed to go off. Don't let spectators bring their own fireworks onto the site. Discourage spectators from bringing drink onto the site.
If you will also have a bonfire at the display then you should:

After the event:
Carefully check and clear the site. Dispose of fireworks safely. They should never be burnt in a confined space (e.g. a boiler)

Major public displays:
For major displays, particularly those involving category 4 professional fireworks or very large number of spectators, a more robust approach is obviously needed. Plan and mark out the areas for spectators, firing fireworks (and a safety zone around it) as well as an area where the fireworks will fall.
Think about how people will get into and out of the site. Keep pedestrian and vehicle routes apart if possible. Mark exit routes clearly and ensure they are well lit. Ensure emergency vehicles can get access to the site. Appoint enough stewards/marshals. Make sure they understand what they are to do on the night and what they should do in the event of an emergency. Contact the emergency services and local authority. If your site is near an airport you may need to contact them. Signpost the first aid facilities.

Registration and licensing:
If you wish to use the fireworks for a commercial display or for some other work purpose, or you wish to store a larger quantity of fireworks, or more powerful fireworks, then you will normally need to register or licence with your local licensing authority. If you wish to buy more than 50 kg of fireworks you will need to produce your registration certificate or licence.
Depending on the specifics of your event you may require a premises or other license. Contact your local council for advice.

Although it is not required by Health and Safety law, if you are holding a public firework display it is a good idea to have public liability insurance. Bear in mind that not all companies are used to dealing with this type of event, and, as with any other type of insurance, it is worth shopping around. Look for a company that is used to insuring firework and other public events, you are likely to get much better deal and avoid unsuitable terms and conditions. If you have difficulty with the standard insurance terms, talk to your insurer and find a way forward; they can be very helpful.