People will give different perspectives on this, ranging from what to pack, to books to read, to spiritual advice.
In my view, the most important thing is to set a sincere intention to do it for the sake of Allah, and to meet the luminaries whom Allah has blessed us with. Then, to remain open to the experience.
Remember also that the experience of ziyarat differs from time to time, based on where we are in our lives, and rather than expecting it to always be the same, be open to change.
Also, ziarat often has a strong social component, insofar as it is an opportunity for believers from around the world to build ties with each other. So it is nice to be open to that and to come with a spirit of acceptance of people, despite their flaws or different cultures and viewpoints. One can sometimes meet lifelong friends at these times.
At the same time, it is better to try to avoid getting dragged into the trap of focusing on social expectations or interpersonal situations between yourself and whoever you may be travelling with, since this can be a distraction. Rather, keep the focus on Allah and the awliya and simply try to treat others well.
There is nothing wrong with performing ziarat in the hope that a specific personal prayer will be answered. However, sometimes, focusing only on that can lead a person to miss out on other aspects of the experience, or be focused only on themself. So it is good to pray for what you need, but also be open to what is happening beyond that.
It is also good to try to find compatible travelling companions, since those who you are travelling with can strongly impact the experience, for better or for worse. Also keep in mind that hajj and ziarat sometimes stress people in different ways (perhaps also due to the strong spiritual energy behind it), and while ideally people should be more patient and forgiving in the holy sites, sometimes it brings out their difficult side. It can also bring out our own weak points. So be prepared to be patient!
In my view, it is not the most important thing to have a strong factual knowledge of everyone and everything about the sites you are visiting, because if you don't have that already, you will pick it up as you go, or be inspired to learn more. However, it doesn't hurt.
There is a lot of material online available, which you can find if you search; here is a nice short piece: https://www.al-islam.org/articles/how-make-most-ziyarah-ahlul-bayt-salim...
Also, you can read some hadith about ziyarat and the spiritual etiquette of ziyarat, or listen to some lectures online.
May your ziyarat be accepted!