Emma is a snob because of the manner in which she treats others. She is condescending toward Miss Bates (a kindhearted but eccentric spinster) and ends up reducing Miss Bates to tears because of her own superior attitude. Similarly, when Jane comes to town, she dismisses her without even getting to know her (because Jane is a rival in beauty and accomplishment). Most significantly, Emma is snobbish toward Harriet who is supposed to be her friend. Even though Emma seems to want what is best for Harriet, she assumes that she would know better than Harriet (based solely on her high opinion of herself and because she holds a higher position in society than does Harriet). Harriet agreeable goes along allows Emma to discourage (at first) from associating with Mr. Martin because he is "common" and a farmer.
Fortunately by the novel's end, Emma has matured and realized her flaws, and most of the effects of her snobbishness have been righted (Miss Bates forgives her; Jane makes a respectable marriage match for love, and Harriet and Mr. Martin marry).
I think you can look to chapter 1 for some very clear examples. First, Emma is introduced as "clever, handsome, and rich, with a comfortable home and happy disposition." She is 21 years old and has had, so far in life, "very little to distress or vex her." Essentially, she's smart, pretty, rich, happy, and has lived a fairly easy life.
The narrator goes on to say, however, that Emma possess "the power of having rather too much her own way, and a disposition to think a little too well of herself." In other words, she's spoiled and selfish.
Combine this introduction with her short-sightedness in dealing with other characters throughout the story, and Emma certainly comes across as a bit of a snob.