I’m often asked to recommend tutors in subjects that I don’t teach, and that’s one way to find a tutor. In fact, word of mouth/personal recommendation is probably one of the best ways to find a good tutor. If a friend at school is using a tutor and is pleased with the results, that tutor may work out well for you too.
There are several reputable agencies which offer a good service although this may not be the cheapest option. When I lived in Surrey I occasionally worked for Surrey Tutors and Wey Tutors and was happy to recommend them.
There are also many online agencies such as Tutor Pages where you can find lists of local tutors with their contact details.
Some tutors advertise in local papers, parish magazines, local halls or even shop windows. Many, like myself, back this up with their own website. Hopefully this allows a prospective parent/pupil to learn more about the tutor and get a feel for their personality and style of teaching.
Evidence of experience and some testimonials from satisfied customers is something to check for, as well as the more obvious qualifications.
Don’t forget not every tutor will suit every pupil. Tutors understand that. Don’t be afraid to try another tutor if things don’t work out. I never expect pupils to sign up to a course of lessons straight away.