First off, start by moving the Random class instance to outside the method - make it a Private class level variable instead. That way, you aren't creating it each time he presses the button, so you should get a better random sequence.
Then, create a List of integers and fill it with the ball numbers. That's easy:
Dim balls As List(Of Integer) = Enumerable.Range(1, 49).ToList()
Then generate six random numbers from the list:
Dim balls As List(Of Integer) = Enumerable.Range(1, 49).ToList()
Dim winner As New List(Of Integer)()
For i As Integer = 0 To 5
Dim winBall As Integer = Random.[Next](0, balls.Count)
winner.Add(balls(winBall))
balls.RemoveAt(winBall)
Next
Becaue you use a list of all balls, and remove each one when it's selected, you are guaranteed not to get any repetitions.
Then all you have to do is sort the user input numbers, sort the winning ball numbers, and you can compare them very simply!
Make sense?