Extract a character at particular place in a string
According to MSDN, this function is already implemented:



' Code from MSDN
'
Dim myString As String = "ABCDE" 
Dim myChar As Char 
' The value of myChar is "D".
myChar = myString.Chars(3)



A review of your code


Please indent your code.
I would choose another, more meaningful name for your function: getCharAt or getByteFromString. It is now clear that the function operates on a string.
I would use the clearer parameter name str instead of s.
"Compress":

place = place + 1
getbyte = Mid(s, place, 1)

' change to
getbyte = Mid(s, place + 1, 1)


The first version is definitely not wrong or ugly, but why use an extra line if we could express the same logic in the same clear manner?
You could use If to shorten your code:

Private Function getbyte(str As String, ByVal place As Integer) As String
  getbyte = If(place &lt; Len(str), Mid(str, place + 1, 1), "")
End Function