Not sure this is the same correct way but I was told to make sure you follow each tooth down. AKA floss pulling towards the front and then towards the back of your mouth.

If I'm going to floss at all, floss then brush. I've found that daily flossing for a week or so before a cleaning is enough to reduce any gum bleeding to a minimum if they 'chart' (check how the gums are doing by poking at them (mesial, distal, lingual, ow).