You personally don't investigate it as you don't have the access to do it. You need to get your telephone company involved, because there's no way for you to determine this on your own. If this is a mobile phone then it's likely someone has cloned your sim card, and you will need to get a new one from your provider to get it to stop. If it's your land line it's more complex to solve, in many places you can spoof a phone number using specialized equipment which is not that expensive anymore, but again it's your phone company who would investigate the source. If the source is outside their network it could be hard to trace.
Another path to a solution would be to determine who would want to do this. What's their goal? If you can figure that out then you probably know who is doing it, if you have a theory then take it to law enforcement as that's their job.