Marriage while incarcerated is possible in many state DOC systems and in the federal Bureau of Prisons, but it is a process that requires patience and a willingness to navigate significant administrative hurdles on both ends.
The starting point is always the chaplain on the inside. Your fiance needs to approach the chaplain directly and express the intention to marry. The chaplain is the person who manages marriage requests at the facility level and knows exactly what the institution's rules and requirements are. If the facility permits inmate marriages, the chaplain will provide a list of what needs to happen and who needs to approve it before anything moves forward.
From there the process typically involves a formal application that works through facility administration and ultimately requires warden approval. On your end, the outside requirements usually include obtaining a marriage license from the county where the facility is located, providing identification documents, and in some cases completing a background check as part of the visitor approval process if you are not already on the approved list.
The timeline from initial request to actual ceremony can stretch into months. Facilities move at their own pace on these requests and there is no way to rush the administrative review.
Here is the honest advice. If his sentence is not extremely long, waiting and having a real wedding on the outside is worth serious consideration. The process of getting approved inside is lengthy, the ceremony itself is typically brief and without the trappings of a normal wedding, and the paperwork burden falls heavily on you. If a proper wedding matters to both of you, it may be worth waiting for the real thing.