The first thing that you need to do is to confirm that the writing, drawing or mark on the paper that you are trying to erase is made from a colored pencil. The method for erasing coloured pencil from a paper is completely different from the method to erase marker or Sharpie from paper. If you messed up while using a marker, you will have to use some other method to erase it.
After you have confirmed that the writing, drawing or mark that you are trying to erase from paper is indeed from a colored pencil, visit the nearest stationary shop and purchase a colored pencil eraser. You will find colored pencil erasers in different shapes and colors. Choose the one that you find the most appealing. Remember, they all perform the same function, so it does not really matter what color or size of colored pencil eraser you eventually buy. Ask the shop-keeper to help you locate the section of the shop where the erasers for colored pencils are displayed, as you might find it difficult to differentiate between the normal pencil eraser and the type of eraser that you are searching for.
If the colored pencil eraser you purchased in the previous step does not do a very good job of erasing colored pencil from the paper, you can try to use a normal pencil eraser on it. This may initially come off as an act of sheer desperation, but it has proven to be very effective. A lot of kids who do not have an eraser for colored pencils use the normal pencil eraser and get the desired result.
If you have tried both the colored pencil as well as the normal pencil eraser, but neither of the two worked for you, the only option that remains is to get a new paper. If the paper was given to you by your teacher, ask her to give you another one.