Tutoring Agencies
Agencies can be a good starting point for finding a private tutor. If you have a child with a specific learning need, for example Dyslexia, it is valid to ask the agency whether they have any specialist tutors. Many will, and hopefully there will be tutors with some excellent qualifications on their books.
Ask at the school
If you don't mind 'going public' about having a tutor then another good place to start is your child's school. Ask other parents if they know of a good tutor in the area. It is always useful to have a recommendation and it saves time asking some of the most basic questions if you know they are doing a good job elsewhere.
Teacher at the school
If there is a teacher at the school who your child particularly likes, then consider asking him or her. They will be pleased to be asked and they may have an evening free when they could help your child.
The Internet
The internet is of course readily accessible now and some independent tutors will have their own websites where you may be able to see their qualifications, teaching experience and what other happy parents/children have said. Simply Google the area you live plus 'tutor' or 'maths tutor' and see what comes up. If the tutor is serious, you should be able to get a decent feel for the person from their website.
Yellow Pages
In the UK we have the Yellow Pages, a hefty book crammed full of local people and their businesses. Look under Tutoring or Dyslexia Support.
The right private 11 plus can really help your child with confidence issues as well as a specific subject matter. Good luck in finding the right person for your child.