North Wales Shooting School
Fauxdegla
Catton Hall
Bolton
Mickley Hall
Several others about.
How to start. Use the CPSA web site to 'find a club' close to you, contact them and book a lesson or a 'have a go' experience. Their website has a few pages on how to get started by the way.
https://www.cpsa.co.uk/how-can-i-try-clay-shooting
Decide if you want to get involved. ( usually this is an irresistible force rather than a decision! )
Have a few lessons, join a club, join the CPSA to show insurance and some alignment with organisational rules, apply for a ticket.
Be prepared to part with anything from a few hundred to a few thousand for your initial gun and few slabs of cartridges.
Set aside a significant portion of your disposable income to buy shells, guns, chokes, clothing, accessories such as bags, slips, stands, ear defenders and glasses and snazzy glasses!
I'd offer to show you around one or two of the grounds but until I'm settled into a new house ( end Feb? ) up here shooting is taking a seat right at the back of the bus!