Make sure you provide plenty of entertainment to get your kids to sit still!
There is no point attempting gorgeous new hair styles if they move after 30 seconds. Keep some special toys that are only brought out at styling time.
If they are still the right age for a high chair pop them in with some snacks and toys - the Fat Brain Whirly Squigz are great as they suction on to the high chair tray and keep them super entertained!
For kids no longer using high chairs I recommend getting them some breakfast organised first then pop on their favourite show for 10 minutes so you can style without interruption!