Whenever considering a hairstyle or haircut, it is important that you pick a hairstyle which focuses on your best facial feature. Also, some practical things like the haircut suiting your lifestyle and hair type is important. If you are looking for round face shape hairstyles, then it will be good to first understand this face shape.
Round face is a full-looking face, that has a round chin and hairline and the widest point in the round face is at the cheeks and ears. So, pick a hairstyle which covers up the cheeks a bit or completely and adds volume to the crown by layering, so that the round face looks longer.
It is an ideal haircut for thin hair helping add volume to it with a low upkeep. Hair on the sides and back are cut too short with front hair kept long, styled to swept bangs. Check pictures of Rihanna and Winona Ryder's haircut.
Get some layers cut near your crown, so that your face looks longer. Then cut your hair on the sides into deep layers, so that they fall on your cheeks. Then complete this hairstyle by adding some blunt side bangs.
For this, cut your hair short near the nape of your neck keeping the side hair longer (symmetrical to look sober/ asymmetrical to look stylish). Add blunt long bangs to finish the look.
So, pick a haircut which suits your hair type and lifestyle and approach a stylist to get a great haircut. If you are having a bad hair day then use few accessories and style your hair into a pony or braid, and for a party style the hair into an elegant updo.