Where exactly are you having problems with what you are doing? You'll need to use different objects and make a few syntax changes, but your logic should not need to change. Firstly there is no recordset object any more, you'll need a datareader to go thru the records. Here's what I came up with. I just plugged your code into VS.Net and changed the syntax where needed until I didn't get any design-time errors, I didn't actually execute it.
Dim arrID(1, -1) As String
Dim strID As Int64
Dim i As Integer = 0
Dim objDR As SqlClient.SqlDataReader
If objDR.GetInt64(0) <> strID Then
strID = objDR.GetInt64(0)
ReDim Preserve arrID(1, i)
arrID(1, i) = objDR.GetInt64(0).ToString
i += 1
arrID(0, i) = arrID(0, i) & ", " & objDR.GetString(1)
Hopefully that will get you off to the right start. If you are using a data provider other than MSSQL than you'll need to adjust accordingly.