Its usually used when you are comparing a topic at hand to a similar topic. For example, Marcus is as tall as Jim. The lady is as old as my grandmother. Sometimes, it is used for exaggeration: The light was as bright as the sun. Her dress was as big as a tent.

This is often used in comparisons .... "her eyes were AS blue AS the sky" .... "she was AS light AS a feather" .... The comparison normally is suggesting that the two things have a quality which is the same or similar.

You can use as ... as to make comparisons with adjectives and adverbs. Tom is as tall as Mary. (They are both 160 cm) Lisa ran as fast as Bill. (They both ran 1 km in 5 minutes.) The negative form is not as ... as. My phone isn't as expensive as an iPhone. (My phone costs $100 and an iPhone costs $500.) She doesn't wake up as early as Jill. (She wakes up at 7:00 a.m. and Jill wakes up at 5:30 a.m.) You don't have to use the second "as + noun" if people already know the two things that you are comparing. Peter is older than Bill, but he isn't as tall. (= Peter is not as tall as Bill.) Mark studies Spanish harder than Joe, but he doesn't speak as well. (= Mark doesn't speak Spanish as well as Joe.) You asked about the sentence, "She doesn't want it as me." The grammar is not correct in this sentence. You must put an adjective or adverb after "as." You also must put "as" before the second thing in your comparison. For example, "She doesn't want it as BADLY as me."