What sort of shooting do you want to do? There are many different disciplines:

Target Shooting:

Air Pistol/Air Rifle - paper targets in your garden/at a club
Gallery Rifle/Fullbore Rifle/Muzzle Loading Pistol - paper targets at a Home Office approved club
Shotgun - clay target shooting at a club/on private land

Game/Rough Shooting incl. Vermin Control:

Air Rifle, Shotgun, Rimfire Rifle - rabbits/pigeon etc
Centrefire Rifle - foxes/deer etc

For air guns up to 12 Ft/lbs muzzle energy, you do not need a licence. I would advise that you join a local airgun club to learn the basics of safety and marksmanship
For smoothbore guns - ie shotguns, you need a shotgun certificate. I would advise that you find a local clay shoot and visit - they will help you
For rifles and muzzle loading pistols, you need a section one firearm certificate and must satisfy the Police that you have a 'good reason' - ie are a member of a target shooting club/have permission to shoot rabbits on a farm etc. Join a Home Office approved club to learn the basics of safety and marksmanship

I am the secretary of a very large Home Office approved target shooting club in the south of England - please feel free to IM me and I will do my best to advise you.