Dental implants are one option to consider when replacing a lost tooth.  They can be used to replace a single tooth, to provide an anchor to hold a bridge, to support replacements for an entire jaw or to give stability to full dentures.
My own feeling about implants is that an implant is a wonderful way to replace teeth where
1.  An implant is really necessary;
2. The implant patient is healthy and cooperative and does not smoke;
3.  The surgeon and restoring dentist are experienced and knowledgeable about the implant procedure and are able to work together smoothly and use the same implant system;
4.  The patient is fully informed about all available options for his or her case. 

Before an implant case is initiated,  there must be a thorough workup including a medical exam, x-rays, etc.  Often, CT scans are used to get a 3-d idea of how the jaw bones are shaped and where implants can be placed, whether there is enough bone, etc.  A treatment plan should be formulated, and the patient needs to be fully informed about any other options, costs, timelines and discomfort.

In cases where there is not enough bone it may be necessary to add bone, possible "lifting" the floor of the sinus on the upper jaw and adding bone to the lower jaw.  This involves additional surgery and questions about whether natural bone or synthetics will be used, healing time, cost, etc.

A dental implant is a metal cylinder that is placed surgically in the jaw bone and it takes the place of a tooth root. Implants are made of bio-friendly materials, titanium being frequently used. Surgery is required to place the implant into the jaw bone. The bone is given time to grow around the implant (integrate with the bone, or osseo-integrate). During this initial phase, no force is placed on the implant. (Temporary crowns may be used to fill the spaces for esthetic purposes.)   After 3-6 months, assuming integration has taken place, the implant is "restored."  That is, a tooth like replacement is screwed into it. 
Usually, two dentists are involved in treatment.  Surgery is done by an oral surgeon or a periodontist (gum specialist).  The restorative part (crowns, bridges, dentures) is done by a general dentist or a prosthodontist (specialist in crowns, bridges, dentures). 

There are some newer procedures in which implants are done in one stage, rather than two.  That is, they are restored right after placement.

The top drawing to the left shows a common implant design.  The lower part is placed in the bone in a surgical procedure.  After the bone grows around it and it is stable, the top portion is screwed in.  A dental crown (or bridge anchor crown) is placed on it.

The bottom drawing shows a perfect indication for an implant because there is no natural tooth present to hold this bridge.  The alternative would be a removable partial denture.  Here, a three-unit bridge is permanently cemented to an implant in the back and a natural tooth in the front, in order to provide for three back teeth where the patient started with only one.