First, use an established and widely used logging framework like log4net or NLog.
Both of the logging frameworks can send log messages to multiple destinations, e.g. to a log file, a network stream (TCP or UDP) or a database.
Then use a log viewer like Log4View to visualize and filter the log messages.
If you use Log4View, please make sure that you create XML formatted log files. Although Log4View can also parse (human readable) pattern formatted log files, XML formatted log data is easier to configure and faster to parse.