You can use a simple SendMessage API to achiev exactly what you want. Let's assume that you have a ListBox and a TextBox where you type in your search text:
Code:
Private Declare Function SendMessage Lib "user32" Alias "SendMessageA" (ByVal hwnd As Long, ByVal wMsg As Long, ByVal wParam As Long, lParam As Any) As Long
Private Const LB_FINDSTRING = &H18F


Private Sub Text1_Change()
    List1.ListIndex = SendMessage(List1.hwnd, LB_FINDSTRING, -1, ByVal (Text1.Text))
End Sub
When you type into the Textbox, it will search the Listbox for the string you typed in. If it finds it, then it will select that list item.