How to Correct a Receding Chin of a 14-year-old?

Without photos and an exam it is impossible to give you accurate advice. It is possible that you will get some correction naturally due to your young age. If this does not occur in the next few years a chin augmentation is a relatively simple procedure successful for most patients but depending on the nature of your chin absence of projection, an othognathic surgery called a sliding genioplasty may be indicated after orthodontics

If your teeth are in alignment than jaw surgery to move your teeth may not be necessary. If your teeth are not in alignment than you may need to have jaw surgery to move your teeth and jaw. In either case, sometimes the chin bone can be cut and slid forward to make it appear larger. Alternatively, you can have a chin implant made form your own tissues or foregn materials. Prices will vary tremendously.

It all depends on your bite.
Edward Angle was the first to classify malocclusion. He based his classifications on the relative position of the maxillary first molar. The mesiobuccal cusp of the upper first molar should rest on the mesiobuccal groove of the mandibular first molar.
* Class I: Here the molar relationship of the occlusion is normal or as described for the maxillary first molar, but the other teeth have problems like spacing, crowding, over or under eruption, etc.
* Class II: (retrognathism, "overbite") In this situation, the upper molars are placed not in the mesiobuccal groove but anteriorly to it. Usually the mesiobuccal cusp rests in between the first mandibular molars and second premolars. There are two subtypes:
o Class II Division 1: The molar relationships are like that of Class II and the anterior teeth are protruded.
o Class II Division 2: The molar relationships are class II but the central are retroclined and the lateral teeth are seen overlapping the centrals.
* Class III: (prognathism, "underbite" or "negative overjet") is when the lower front teeth are more prominent than the upper front teeth. In this case the patient has very often a large mandible or a short maxillary bone.
If you have malocclusion, orthognathic surgery could improve your chin position especially if you have a class 2 occlusion where the top jaw is more anterior than the bottom. Correcting this can project your chin forward.
If you have a Class one occlusion, and your chin is still posteriorly situated you have what is called retrogenia or microgenia, a chin implant could improve the appearance of your chin. Sometimes, correcting a malocclusion can still leave you with a small chin and an implant may still be needed. Genioplasty is the actual movement of the bone in a forward and inferior direction to increase the chin size vertically and horizontally.
Chin implants can only increase the vertical dimension approximately 2mm anymore usually has traditionally required a genioplasty. Although there are custom implants that can give you more vertical height of your chin. Genioplasty is a significant surgery and many people feel it is more work than worth the recovery. Chin implant recovery is much less than a genioplasty in most hands.
You should come in to discuss this with someone qualified to consult you about this.