The first thing is to analyze the length of your hair and check what your boundaries are, means the length of your hair. If the length of your hair is long or medium then you have variety of hairstyles which can be made. According to your hair length try looking for hairstyles which are in fashion or which will suit you.
If we talk about the style which that suites you then analyze your face shape. Your face curves should be made soft and try opting a style which will help in enhancing your facial beauty. Try not going for a hair style which will make your face curves more prominent.
For searching purpose check different magazines and internet, latest movies and TV. See which style is in fashion these days, but keeping in mind the factors mentioned above.
If you have chosen a hairstyle which was found on internet then try taking a print out of the image or if the desired image is in the magazine then you can show the magazine to your hair stylist. This is the best way to explain what sort of style you are wishing to have.
Try using hand gestures while explaining the haircut to your stylist, like the length of the layers, fringes etc.
Try listening to the suggestion of the hairstylist as well he is the one who can recommend you a best hairstyle that will complement your personality.
After having the hair cut ask the stylist to give you a back mirror so that you can check whether the haircut has been done appropriately or not.