SQL Server, by default, will store logs under \MSSQL\LOG folder where you have your SQL Server program files installed. On an active server, you'll often see log files named from 1 to 6 (depending on max number of logs). The log without a number is the current one and the log with the lowest number is the most recent.
You can force SQL Server to cycle the logs by calling sp_cycle_errorlog from query window. SQL Server will flush out the last log to disk and shift the log numbers.