You cannot issue a subpeona. You need to get a lawyer. Contact the Clerk of the Court where you have your lawssuit and assk them if they asssist people in serving subpeona's. They will probably tell you they cannot help you because they cannot give legal advice.
As a Florida lawyer, I disagree with the previous opinion. You can subpoena a witness pro se in Florida. You have to do it right, though.
The problem is that doctors are a kind of special class of witness. Doctors are expert witnesses if you are calling them to testify to things medical. Expert witnesses are entitled to get paid for their services by the hour. Typically a doctor can demand a thousand dollars to testify. And if you don't pay what the doctor demands, he won't testify. And even if you were to get the judge to force the doctor to testify for a reasonable fee, how would you expect your doctor to testify in your favor.
Also, typically, you do not actually call the doctor to testify in court because you have to pay for his waiting time and because of his scheduling (he has to be available to "save lives" and perform operations, don't you know.). So what lawyers do is they take their depositions in the doctor's office. And if they really want to do it right they take a video deposition of the doctor in his/her office. Video depos cost even more. You have to pay the video technician and the doctor wants more money for a video of his puss. Last one I did I had to pay the doctor $1500 for less than an hour's time. Then at the trial time they play the video to the jury, or they read the deposition to the jury.
But to take a doctors deposition you really have to know what you are doing. You have to know what questions to ask. There is a legal "ritual" to getting the testimony of an expert witness admitted and to asking admissable questions. You have to know the medical terminology. Even if you are representing yourself in trial, you should hire an attorney to take the deposition of a doctor. It costs too much to do it wrong.
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I agree with Mr. Picchi's answer. There is a relatively simple process for getting a subpoena issued by the court, and you can hire a process server to serve it. But to get something you can really use, you'll need to know how to get the doctor to appear, and what to ask. As a theoretical matter, you can do this yourself. As a practical matter, it is going to be more effective to get a lawyer.
Please note that nothing herein is or may be relied on as legal advice. Each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.