The problem is that you have your textboxes initialized to strings, which cannot be converted into doubles, so VB complains. The quickest way to make VB ignore this is to add the line:
at the top of the sub. This tells VB to continue on to the next line when an error arises. It certainly is not the best way to handle errors, but until you decide exactly what you want to do, it will work. So, applying it to your program, it would look like this:
Private Sub optaddition_Click()
On Error Resume Next
Dim dblNumber1 As Double
Dim dblNumber2 As Double
Dim dblResult As Double
dblNumber1 = CDbl(txtnumber1.Text)
dblNumber2 = CDbl(txtnumber2.Text)
dblResult = dblNumber1 + dblNumber2
txtresult.Text = dblResult
End Sub
If you need more help on Error Handling, let me know, and I'll try to explain to you how it works. It's not hard.
Hope this helps.