The logistics of a visit are one thing -- how a child feels about it is another, and it's worth just as much prep.
Explain what's actually going to happen
Kids handle new, intimidating-sounding places much better when they know what's coming: there will be a security check (like at the airport), a waiting room, then a visiting room with tables and chairs. Naming it in advance -- "we'll walk through a metal detector, that's normal, everyone does it" -- takes a lot of the scariness out of it.
Prepare them for the contact rules
A hug and kiss at the start and end, hands on the table in between. If your child is used to climbing into a parent's lap or roughhousing, tell them ahead of time that this visit works differently, and that it's not because they did anything wrong -- it's just how every visit works for every family in that room.
It's normal for it to be hard
Kids might get quiet, clingy, silly, or upset -- during the visit, or afterward once the adrenaline wears off. None of that means the visit was a bad idea. It usually means it mattered. Give them space to feel however they feel about it rather than needing them to perform "happy" the whole time.
After the visit
Saying goodbye is often the hardest part, for kids and adults both. A simple, honest script helps more than a cheerful deflection: "That was hard. I miss them too. We'll see them again." Kids take their emotional cues from the adults around them more than from the visit itself.
(See also the pinned guide "For Caregivers: Helping a Child Understand and Cope" in Guides → Emotional Support for the bigger picture beyond just visiting.)