It is actually really easy. The process server merely needs to go to the prison or jail and serve as they ordinarily would. They just need to notify the person at the desk that they are serving legal papers, and they will either sign for it or get the designated person to come and get them on behalf of the inmate.
You can also work through the Sheriff's office to have the papers served, as opposed to a private process server. When you get your proof of service back from whoever performs the service, you need to file that with the court.
You may be mixing up the facilities, as jail and prison are two different entities. If he is in prison, then most prisons have a legal coordinator whom you can contact and he or she will assist you with that process. If he is in jail, then usually you can have the process server show up at the jail and there is typically a clerk that only needs to be informed that they are there to serve legal papers.
However, the one point I would add to my colleague's responses, is that you may want to have someone over the age of eighteen, other than yourself, do it as a favor for you. This is because there can be many occasions where the jail is on "lock-down" or the inmates are at "meal-time" or there is not an available deputy to pull the inmate at the instant the process server arrives.
Thus, as an attorney, I have served people in the jails and had to wait in upwards of an hour or more while inmates were on lock-down, at mealtime or another incident was happening that simply made all the deputies unable to be assist at that instant. I do not want to alarm you with that last part of my answer, but just do not want you to have any surprises. Good luck.