Obtain a sample of the fragrance you like. You can use a magazine sample, or hit up the perfume counter at a department store and ask for a small vial. Perfume-counter employees may also be able to help you find alternatives to discontinued fragrances.
Observe the smell of the fragrance. What do you like about it? Write down the "notes" you notice in the fragrance, such as citrus, floral, musk, woodsy, earthy, and food scents.
Determine which of the main fragrance groups your scent belongs to. The groups are: aldehydic, similar to Chanel No. 5 or Estee Lauder White Linen; chypre, a combination of woody and floral tones; citrus; floral; fougere, woody and herbal scents commonly found in men's fragrances; Oriental or ambers, with musk and vanilla bases; and woody, with bases of cedar, patchouli, sandalwood and vetiver.
Go shopping! Look for fragrances in the same group as the one you're trying to imitate. Use the tester bottles to try before you buy. If you're shopping online or otherwise unable to test out scents, read the product description; at least a few of the scent notes should be mentioned. Match those descriptions with the notes you listed from the original fragrance.
Cheaper fragrances may be more watered down or made with lower-quality ingredients than high-end scents; keep this in mind when shopping for "designer impostors."
Some fragrances may irritate your skin or cause an allergic reaction.