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.
ERRORLOG
ERRORLOG.1
ERRORLOG.2
ERRORLOG.3
ERRORLOG.4
ERRORLOG.5
ERRORLOG.6
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.