Hi there! Well as someone who has plenty of experience in the subject and has moved international museum exhibitions, I can tell you the first thing you have to do is to have the curatorial script. For such a thing, you need to know who is going to be the curator of such, because whoever does that job will have a vision of what he/she/they wants and what pieces to include.
Then you need to ask the curator to create the artwork list. With such, you will know where the pieces are. Most curators already have a relationship with the collections (whoever owns and has the art pieces). If not, that just know where the art piece is, you will have to be the cultural manager that create the relationship with the collector (there are many steps before but is just to give you a broad idea).
I assume you will have already the venue, if not, you will need to secure the venue where the exhibition will take place, which could be a Museum or Gallery. Keep in mind that most collections (at least if the pieces have been in museums already) require certain conditions for the venue to have and they will require a facility report for the loan that fulfills their requirements (security, temperature and humidity factors, etc).
Then you will need to consider insurance for each piece and transportation (you will need specialized art transportation, don't worry there are a few out there).
All require a cost, so you will need to consider a budget. Sometimes collections will lend you for free their pieces, and sometimes they will charge a fee or something in exchange (like a catalog which is usually required).
Then you can start contacting the institutions and request the pieces. If you are planning to do a more art collective exhibit, that might be easier than museum. There are a lot of things to consider to make all successful. It might be daunting, but that is why there are people like me that can help. I have moved all sorts of exhibitions ( I was Head registrar at Museo del Palacio de Bellas Artes and because of it, I had to move pieces from Europe like the Boijmans Museum, Tate, National Portrait Gallery, Pompidou Pushkin Museum, and even the Vatican when I was a Museum director. I've also moved pieces from local collections and in the US like from LACMA or the Met). I hope this information helps and let's book a call!