How to log a stored procedure error

IF @@ERROR <> 0 ...

DECLARE @ErrorCode INT

INSERT INTO Table ...

SET @ErrorCode = @@ERROR
IF @ErrorCode <> 0
BEGIN
    INSERT INTO ErrorLog (ErrorCode, Message)
        VALUES (@ErrorCode, 'The INSERT operation failed.')
END

RAISERROR ... WITH LOG

xp_logevent {error_number, 'message'} [, 'severity']

ALTER PROCEDURE [dbo].[StoreProcedureName]
(
parameters
)
AS
BEGIN
    SET NOCOUNT On
    BEGIN TRY
        --type your query

    End Try
    BEGIN CATCH
        SELECT
                ERROR_NUMBER() AS ErrorNumber,
                ERROR_SEVERITY() AS ErrorSeverity,
                ERROR_STATE() AS ErrorState,
                ERROR_PROCEDURE() AS ErrorProcedure,
                ERROR_LINE() AS ErrorLine,
                ERROR_MESSAGE() AS ErrorMessage
            RETURN -1
    END CATCH
End