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

using Discord;
using Discord.Rest;

public class Program
{
    // Note: This is the light client, it only supports REST calls.
    private DiscordClient _client;
    static void Main(string[] args) => new Program().Start().GetAwaiter().GetResult();
    
    public async Task Start()
    {
        _client = new DiscordClient(new DiscordConfig() {
			LogLevel = LogSeverity.Info
        });

        _client.Log += (message) => Console.WriteLine($"{message.ToString()}");

        await _client.LoginAsync(TokenType.Bot, "bot token");
    }
}