Pin up your hair. If your hair is long, separate the hair into two pieces, and twist. Cross the two pieces behind your head, and clip them across the top. This is an easy way to even your hair out on your head without a huge ponytail bulge. Shorter hair can simply be combed and clipped to the crown of the head, or placed into a bun at the base of your neck. You could also braid your hair before applying a wig
Pin up any bangs. If you have a fringe or side fringe and you cannot get a wig cap, you may find it helpful to wear a small hair band to keep hair from showing under your wig. Elastic ones are the best to use because they are more comfortable and are usually smaller.
Put on a wig cap. For long hair you can use a wig cap to hold it all in and ensure a smooth fit. It will help keep the wig on.
Put the wig on your head from front to back. There are two tabs on each front/side of the wig. Position this right in front of your ears. Don't worry if it doesn't look perfect right away. Go ahead and style/brush it into place the way you'd like it to look.
Accessorize. If you'd like extra coverage, or to add something onto the look you are going for, you can use accessories, such as a jeweled headband if you're dressing up as Cleopatra or Delilah, or a bow tied on the back of your head if you're dressing up as a schoolgirl.