The salesforce administrator at your org can enable the option to Signup and Check-In for the volunteers after searching the volunteer name.

At least one option, Signup or Check-In should be enabled in the V4S Kiosk configuration screen. And if none of these checkboxes are enabled, then the volunteers see the message as "Volunteer will be signed up and checked in" and nothing happens when the volunteer click the text after the volunteer search for their name.

To fix the issue, please ask the Salesforce administrator at your org to enable either Signup or the Check-In button in the V4S Kiosk configuration screen.

V4S Kiosk configuration screen in Salesforce