How Can I Find out How Many Dental Implants a Dentist Has Done?

I would ask to see before and after pictures of similar cases to your own. A single back tooth being replaced by an implant is a relatively easier case than doing a single front tooth being matched to natural teeth. Replacing an entire mouth with implants is also a difficult case to execute properly that requires advanced training.

You could also consider the doctor's credentials and advanced training. 

Ask your friends and family member who they went to. Read any online reviews about the dentist. 

The best proof of your dentist's experience in dental implants can be found in: 
1) Patient testimonies/reviews 2.) Before and After pictures 3.) Doctor education and Certifications
The following questions can also help you determine whether a doctor is experienced with dental implant placement.
1.) Is the dentist experienced in bone grafting?

            How many bone grafting procedures has the dentist completed?

2.) How many surgical training courses has the dentist completed?

3.) How many implants does the dentist place per year?

4.) How long has the dentist been placing implants?

5.) How many continuing education courses on implants does the dentist take per year?

6.) How many courses has the dentist taken focusing on managing challenging cases and/or complications?

7.) Does the dentist refer overly complex or difficult cases to another surgeon?

8.) Did your dentist attend an accredited institution? 

Ask for pictures of their implant cases.  I have collected several of mine for this reason.  Dentists who place implants should be proud of their work and should have many pictures.  That is better than going off grey hair, a title or office appearance.  Otherwise, it's about the trust and assurance you have with the dentist.