If you post more details about what WiFi router and smart plugs you have, then folks here may be able to provide more specific guidance.
Typically, you need to reset the smart plug (to clear existing WiFi credentials it has cached), and then run whatever app the vendor provides to configure it.
What typically happens is that the reset, turns the SmartPlug into a Wi-Fi access point. The app connects to that access point and posts the credentials for the main WiFi network. Having received the main WiFi network credentials, the SmartPlug ceases being an AP and instead becomes a WiFi client like all the other devices on your network. If you want to see what your SmartPlug is doing, you can install a traffic analyzer, like WireShark, and look at traffic on your WiFi network.