Camera in sensor clean mode with well charged battery, couple of puffs of the rocket blower to get rid of any dust inside it and away you go.
Hold camera upside down and then a good few hard squeezes of the blower as you direct the nozzle across the sensor (low pass filter actually) Have read about not putting the tip of the blower beyond the camera mount, but personally want to aim at the sensor so get a lot closer than that.
Don't worry its not made of tissue paper and unless you go mad very unlikely you will ever do any damage. None of that gentle puffs business, you want to get it shifted, not soothe it with a gentle breeze.
Have a check after the intial clean by taking a shot of something light at f/16 upwards looking at 100%, if still showing marks have another go.
I think some people get too obssessed with dust spots and just one of those things that can't be avoided, must be an OCD sufferers worst nightmare.