You can either contact the venue directly and speak to the event coordinator to arrange for the rental of a ballroom, or you can use an event planner or event planning website to arrange the rental for you. Many venues have event coordinators to help with renting ballrooms.
Call the venue directly or look on the website's rental page to find the event coordinator. You will likely need to know some basic information, such as how many people are attending the event and whether you want catering or need any technical assistance.
Some websites, such as eVenues, allow you to search and book venues for events online. When using these sites, you can search venues by location and party size, pick from a list of venues, and then submit an online inquiry about specific dates.
Before booking your ballroom, be sure to ask plenty of questions such as if a deposit is required and if there is a cancellation fee. Also ask if you can choose your own caterer or if there is an in-house caterer or a list of preferred caterers. You may also want to inquire about the venue's insurance requirements, as some require all photographers and other vendors to have insurance.