Though elephants were a diverse and populous group in prehistoric times, today only two species of elephants survive: the Asian elephant and the African elephant. The two can be distinguished by the size of their ears (small for Asian and large for African) and the finger-like protuberances at the ends of their trunk (one for Asian, two for African).
So you want to be a classic, no-frills elephant or dress your child up as one. Start with a gray hooded sweatsuit or romper, or, for a baby or very small child, trace the wearer's body on a piece of grey fabric, cut out two shapes and sew them together to make a suit. For ears, cut out elephant-ear shapes from a piece of stiff fabric or grey cardboard and sew them to the hood of the sweatsuit or a headband. Paint the insides pink, if desired. For a trunk, either purchase an elephant nose from a costume store or collect cardboard toilet paper cores. Cut the cores in half, paint them grey, punch two holes in each end of each piece and tie them together using string. Then attach one end of the chain to a piece of elastic, which can be attached over the wearer's nose. For a tail, attach a piece of gray, frayed rope to the costume's rear end. For tusks, roll pieces of white craft foam into long cones, tape or glue them closed, and attach them to the sides of the hood. For elephant feet, paint large work or combat boots gray. To be a pink elephant, follow the same instructions but replace everything gray with pink.
For Halloween and regular costume parties, sexed-up versions of animal and character costumes are popular amongst women. To dress up like a sexy elephant, begin with a sassy gray, silver or pink dress or lingerie ensemble. Follow the instructions in Section 1 regarding the trunk, tail and ears (attach the ears to a headband or even a wig). Add matching makeup -- lots of glitter is especially appropriate. If desired, draw tusks onto your cheeks with eyeliner and white face paint.
If you really want to go wild with your elephant costume, grab a buddy and be a pantomime elephant. Get two gray sweatsuits and cut the arms off the shirts. Sew the holes closed. Get a length of grey fabric and sew it into a tube with a diameter approximately the length of the backs of the sweatshirts. Join the two sweatshirts together by sewing one on each end of the tube. Follow the instructions in Section 1 for feet (for both); ears, tusks, and trunk (for the "head"); and tail (for the "rear"). As this costume is not terribly practical for having a good time, it is not recommended for parties.
The elephant is the symbol of the Republican party in the United States, and there are a few ways to reference that in costume form. Dress up in an "Uncle Sam" getup (blue jacket, red-and-white striped pants, American flag top hat) with an elephant nose as described in Section 1, or add an elephant nose to a rubber mask of your favorite Republican president.