How does a dentist fix a chipped front tooth with filling?

Depends. The size of the chip is important in choosing how to fix it. If it's a small chip, then a resin composite or bonding can be done in a way that blends with the color of the tooth and if done and taken care of properly can last for a long time. If it's a bigger chip, you'd be looking a fixing it with porcelain in the form of a veneer or a crown, as it is a more durable and color stable material.
Poorly. A filling by definition is a "contained" material. It fills a hole. Replacing enamel on chipped edges places bonded composite at risk of separation when brought into function. Biting a sandwich likely will break it off. Bonding composite is a temporary solution. Longevity is important. Small chips respond best to tooth contouring. Large chips to veneering with porcelain. Crown fractures.