What is the process a lawyer goes through to get a subpoena?

A subpoena for a person to appear to give testimony only requires an attorney's signature. 

A subpoena for records or other physical evidence requires the attorney to petition the court and get a judge's signature. 

It depends on the reason for the subpoena and whether or not Government records are involved.  In MY State an attorney representing either party can sign and have the subpoena served.  If Government records are involved the attorney prepares the subpoena and it is signed by a Judge.

Some subpoenas are issued by a lawyer. Others, such as one to be served on a government agency, are prepared by a lawyer but have to be approved by a judge.

Lawyers get a subpoena by "service" or by mail just like anyone else. The process of getting served with a subpoena may involve walking and reaching out and grasping to take the subpoena. The process of getting a subpoena by mail may involve some driving, walking and perhaps opening a mailbox.