Summarize:

You can color extensions made from human hair yourself, but it's best to use semi- or demi-permanent colors because they're not as damaging. Lay them flat and apply the hair color, attempting to match the color to the ends of your hair, rather than the roots. If you want your extensions to look really believable, take them to your hair stylist and have them cut and colored professionally. Do not attempt to dye synthetic hair extensions, as they can be ruined. The hair bonding glue will adhere better to your hair if it's free from any oils, so be sure to shampoo your hair thoroughly. In addition, your natural hair will be hidden under the extensions for as long as you have them in. Deep conditioning your hair in advance will help your locks stay nourished and healthy. Your hair should be completely dry before you apply extensions, so either blow dry it or allow it to air dry. You'll get a more even application if the extensions lie straight on your hair, so be sure both your hair and the weft are free of tangles. The extensions are made to be treated like real hair, so although you should be gentle, it's okay to comb them the same way you would your natural hair. It may help to lay the extensions flat while you're detangling them. If you have curly hair, it may be easier to detangle your hair before you dry it.
Treat your extensions like your own hair if you color them yourself. Wash, deep condition, and dry your hair before applying the track. Gently detangle your hair and the extensions with a comb.