Discord.Net/docs/guides/samples/logging.cs

using Discord;
using Discord.Rest;

public class Program
{
    private DiscordSocketClient _client;
    static void Main(string[] args) => new Program().Start().GetAwaiter().GetResult();
    
    public async Task Start()
    {
        _client = new DiscordSocketClient(new DiscordSocketConfig() {
			LogLevel = LogSeverity.Info
        });

        _client.Log += Log;

	 await _client.LoginAsync(TokenType.Bot, "bot token");
	 await _client.ConnectAsync();
	    
	 await Task.Delay(-1);
    }

    private Task Log(LogMessage message)
    {
        Console.WriteLine(message.ToString());
        return Task.CompletedTask;
    }
}