Discord.Net/docs/guides/int_basics/message-components/responding-to-buttons.md

uid	title
Guides.MessageComponents.Responding	Responding to Components

Responding to button clicks

Responding to buttons is pretty simple, there are a couple ways of doing it and we can cover both.

Method 1: Hooking the InteractionCreated Event

We can hook the ButtonExecuted event for button type interactions:

client.ButtonExecuted += MyButtonHandler;

Now, lets write our handler.

public async Task MyButtonHandler(SocketMessageComponent component)
{
    // We can now check for our custom id
    switch(component.Data.CustomId)
    {
        // Since we set our buttons custom id as 'custom-id', we can check for it like this:
        case "custom-id":
            // Lets respond by sending a message saying they clicked the button
            await component.RespondAsync($"{component.User.Mention} has clicked the button!");
        break;
    }
}

Running it and clicking the button: