La API necesaria para ello es GlobalMemoryStatus, este es un ejemplo, pero podés encontrar un muy buen código para estudiar en
http://www.planet-source-code.com/vb/scripts/ShowCode.asp?txtCodeId=30597&lngWId=1
Private Type MEMORYSTATUS
dwLength As Long
dwMemoryLoad As Long
dwTotalPhys As Long
dwAvailPhys As Long
dwTotalPageFile As Long
dwAvailPageFile As Long
dwTotalVirtual As Long
dwAvailVirtual As Long
End Type
Private Declare Sub GlobalMemoryStatus Lib "kernel32" (lpBuffer As MEMORYSTATUS)
Private Sub Form_Load()
Dim MemStat As MEMORYSTATUS
GlobalMemoryStatus MemStat
MsgBox "You Have " + Str$(MemStat.dwTotalPhys / 1024) + " Kb total of Memory and" + Str$(MemStat.dwAvailPageFile / 1024) + " Kb free of PageFile memory."
End Sub