We are using a third party tool that wants to poll tags that we have in Ignition. What do I need to do to set up their server to be able to poll tags that I have created in a specific tag provider within Ignition?
If this third party tool supports OPC UA, you can configure the Ignition OPC UA Server so that it listens on a public bind address (0.0.0.0) and has the "Expose Tag Providers" feature enabled. Requires a restart to take effect. Ignition's OPC UA Server | Ignition User Manual
Another option would be to use the WebDev module to implement your own API for retrieving tag values. Third party tool needs to be able to make HTTP calls.
Hard to suggest anything else without more information about what the third party tool is capable of.