First-class LLB student at Sheffield with A*AAB A-levels. I tutor primary school children and Year 4-5 students for the 11

My starting point is always understanding where the child actually is, what they enjoy, what frustrates them, and what they're currently working on at school.
For primary-age children, my approach is:

Build confidence first, a child who believes they can do it will learn faster than one who's been corrected too many times.
Use plenty of worked examples, with the child trying similar problems while I watch.
Keep parents updated on what we've covered and where their child is making progress.

For 11+ preparation:

Familiarise the child with the question styles used in the relevant papers (GL Assessment, CEM, ISEB Common Pre-Test, or school-specific exams).
Build exam technique, timing, knowing when to move on, working under pressure
Work through past papers gradually with detailed feedback after each one
Drill the things that actually win marks under time pressure: vocabulary, mental maths, verbal and non-verbal reasoning

I'd rather a child fully understands the reasoning behind one question than memorise five without knowing why they work.