Try this:

[vba]Private Sub Workbook_Open()

usr$ = Environ("Username")

Dim cN As ADODB.Connection
Dim rS1 As ADODB.Recordset
Dim connString As String
Dim returneddata As Variant
connString = "Provider=Microsoft.Jet.OLEDB.4.0;User ID=Admin; _
Data Source=##DatabasePath&Name###.mdb;Mode=Share Deny None;Jet OLEDB:Engine _
Type=5;Jet OLEDBatabase Locking Mode=0;Jet OLEDB:Global Partial Bulk Ops=2;Jet _
OLEDB:Global Bulk Transactions=1;Jet OLEDB:Create System Database=False;Jet _
OLEDB:Encrypt Database=False;Jet OLEDBon't Copy Locale on Compact=False;Jet _
OLEDB:Compact Without Replica Repair=False;Jet OLEDB:SFP=False"

Set cN = New ADODB.Connection
cN.ConnectionString = connString
cN.ConnectionTimeout = 200
cN.CommandTimeout = 200
Set rS1 = New ADODB.Recordset
cN.Open
rS1.ActiveConnection = cN

xqry = "INSERT INTO [###TableName###] ( User_ID, [Date], [Time] ) SELECT '" & usr & "', '" & Date & "', '" & Time & "'"

rS1.Source = xqry
rS1.Open

End Sub

[/vba]

... just replace the ##DatabasePath&Name### with the filepath & name of your Access database, and create a table with the columns 'User_Name', 'Date' and 'Time' and replace the ###TableName### with the Table name.