First, it's important to understand that a Timer doesn't count up or down or anything in between. All a Timer does is raise a Tick event at a regular interval. What you do in the Tick event handler is up to you. You can update a Label with the current time or the time remaining until a specific time or whatever.
So, first you need to get a Date to represent the end of the month:
vb.net Code:
Dim todays As Date = Date.Today
Dim startOfMonth As New Date(today.Year, Today.Month, 1)
Dim endOfMonth As Date = startOfMonth.AddMonths(1)
You'll need to store that result in a member variable so that you can use it repeatedly. To calculate the amount of time remaining until that target, you simply subtract the current date and time from it:
vb.net Code:
Dim timeRemaining As TimeSpan = endOfMonth - Date.Now
That TimeSpan has properties for days, hours, minutes, etc, so you can create a string to display in a Label or whatever.