Before making your Cindy Lou Who costume, you should decide whether you would like to base it on the classic Dr. Seuss book "How the Grinch Stole Christmas" (and the 1966 cartoon based on the book) or on the 2000 movie adaptation of the story.
In the Dr. Seuss book and the cartoon based on it, Cindy Lou Who is seen wearing a pink nightgown. She has short blond hair with red bows and what resembles thin little antennas sticking out of her head. The pink nightgown is down to her feet, with long sleeves, and a scalloped edge collar.
The version in the 2000 adaptation of "How the Grinch Stole Christmas" would make for a much more interesting Cindy Lou Who costume, so I would recommend this over the book's version. However, you can get costume ideas from both sources. Costume making is a fun project that can include your friends and family.
Cindy Lou Who's hair is also very interesting in this movie; most of her hair is in braids, but the top part appears to be covering some sort of cup on the top of her head. You could do this by putting a small cup on the top of the head, and pulling the hair up all around it. Tie with a hair tie tightly at the top. The ends are curled in neat little curls.
This look might not be the best option for those with thinner hair or those who feel dumb with a cup on their head. If you just did a pony tail on the very top of your head, it would have about the same effect. It is important however, that you hair does not look messy. A Who's hair may be in a weird and crazy style, but it always pulled up very cleanly and neatly.
Cindy Lou Who wears a red Christmassy hooded cape. You would probably need to make this; you can find a pattern at a fabric store. Red velvet or some sort of woolen fabric would be good, with furry white trim on the hood. Attach a long ribbon tie to close the cape, with fluffy white balls on the ends of the tie.
Cindy Lou Who's dress underneath should also be Christmas themed. A red and white, or red and green plaid fabric would be good. Look for a pattern for a dress with a knee length full skirt. A petticoat underneath would make the dress even cuter. Red and white striped tights might be a good addition to this adorable costume.
These costume ideas should provide inspiration to make your own Cindy Lou Who costume. Good luck!