Generally scars on the face are the result of acne lesions or injuries. The type of scar determines which treatment is appropriate.
Once facial skin has been injured, e.g. due to an accident or surgery, scar tissue will develop. Most commonly these scars are hypertrophic. This means they are red (or purple/pink) and raised. They may itch and, in some cases, hurt.
The only working treatment for such scars are silicone gel sheets. They are proven effective as demonstrated by various clinical trials and studies. Check out this PubMed study abstract to learn more: Silicone gel sheeting is safe and effective treatment for hypertrophic and keloid scars.
Also silicone gel creams (a popular cream goes by the brand name Kelo-Cote) can improve cosmetic appearance. Silicones make hypertrophic and keloid scars less red, more skin colored, flatter, softer, and they reduce the risk on keloid development as well. Click here for recommended scar treatment products.
Acne scars are harder to treat effectively. There are roughly two types of acne scars. Rolling scars which are slightly depressed and ones that are narrow and deep. Recommended therapies are laser resurfacing, chemical peels, dermabrasion, and (collagen) fillers.
A popular over-the-counter product used to reduce acne scars on the face is Glycolic Acid
In case such treatments do not work surgery may be conducted as a last resort.
Non-acne facial scars will often heal relatively well because there are so many muscles in the face. Regular movement of these muscles as well as optimal blood flow tends to improve the healing process.
Make sure to keep scars out of the sun for the radiation will make their appearance worse. Also hydration (e.g. by using Vaseline or another moisturizer) and massage will aid the healing process.