GETDATE - Current date, Month Start and Month End in yyyymmdd
From SQL Server 2012 you can use EOMONTH (Transact-SQL)

SELECT DATEADD(DAY, 1-DAY(GETDATE()), GETDATE()) AS CurrentMonth_start,
       EOMONTH(GETDATE()) AS CurrentMonth_End,
       DATEADD(DAY, 1, EOMONTH(GETDATE())) AS NextMonth_start,
       EOMONTH(GETDATE(), 1) AS NextMonth_End;