Currently there are 12 root server operators, whose identities you can see at the top of www.root-servers.org home page.
The number of root server instances changes (generally increases) over time. The current count of root server instances is shown just below the map on the home page.
Different operators deploy a different number of instances. You can see the per-operator instances, including their locations, by clicking on the letters at the bottom of the home page.
In each operator's list of sites, some instances are marked as global (globe icon) and some are marked as local (flag icon). The difference is in how widely available that instance will be, because of how routing for that instance is done. Recall that the routes for an instance are announced by BGP, the inter-domain routing protocol.
For global instances, the route advertisement is permitted to spread throughout the Internet, i.e., any router on the Internet could know the path to that instance. Of course, for a particular source, the route to that instance may not be the optimal route, so some other instance could be chosen as the destination.
With a local instance, however, the route advertisement is limited to only nearby networks. For example, the instance may be visible to just one ISP, or to ISPs that connect at a particular exchange point. Sources from farther away will not be able to see and query that local instance.
All operators provide service to the entire Internet through at least one global instance. Some operators may also choose to deploy local instances, depending on their own needs and requirements, and those of their provider partners.
Refer to RFC 4786 (section 4.4.6 in particular) for further details.
You may contact individual operators by finding their published email addresses linked off the home page. Find the Root Servers section and click on the individual letters. Then look on the right side of the page for a blue "Contact Email" or "Homepage" link. You may contact the root server operators collectively by writing to email@example.com.
If you believe that your area of the Internet is underserved with respect to root zone service, you may inquire with individual operators about locating an instance nearby. Root server instances are generally located at data centers and exchange points. Different operators will have different requirements for providing instances at remote locations. Below are some links to pages of operators that offer hosted instances: