I would approach it the same way as recruiting a nanny. You can either go through an agency or look on the Internet for sitters local to you.
If you have any form of childcare, or have used one you were happy with in the past, it might be worth contacting them to see if they'll babysit. Sometimes nursery nurses aren't allowed to babysit under their contracts and CMs don't want to but it's worth a shot. Alternatively friends with nannies or APs may not object to you offering a bit of babysitting.
You then meet them in person, check their ID, DBS check, first aid, any qualifications, ask for references. Call those references to check they're not just the babysitter's mates and ask them questions like 'how would x cope in an emergency?'.
A trial where they come and meet the children one evening, with you having easily cancellable plans to go out, is well worth it if you can afford it.
If it's not someone I know then I prefer someone who works in childcare already because they'll be used to all the checks and questions and have their ducks in a row. They also usually have a reassuring level of experience and given that you're entrusting your children, house and everything in it to them while you're out you need as much reassurance as you can get.
Alternatively you may find by looking round that someone you know babysits but you just never heard about it!
Good luck :)