vba – How do I write a macro to open an excel file and paste data into the file containing the macro?

ThisWorkbook.Activate

should do the trick.
Judging by your macro, paste it after your “‘ select current workbook and paste the values starting at U4” comment.

You need to remember where you came from:

Sub ImportData_Click()

    Dim rDest As Range
    Set rDest = ThisWorkbook.Sheets("Make").Range("A1:Z360")

    ' open the source workbook and select the source sheet
    Workbooks.Open Filename:="C:\TestFolder\Test.xlsm"
    Sheets("Make").Select

    ' copy the source range
    Sheets("Make").Range("A1:Z630").Select
    Selection.Copy

    rDest.PasteSpecial Paste:=xlValues, Operation:=xlNone, SkipBlanks:= _
        False, Transpose:=False

    ActiveWorkbook.Close

End Sub

   Private Sub CommandButton1_Click()
   Dim mode As String
Dim RecordId As Integer
Dim sourcewb As Workbook
Dim targetwb As Workbook
Dim SourceRowCount As Long
Dim TargetRowCount As Long
Dim SrceFile As String
Dim TrgtFile As String
Dim TitleId As Integer
Dim TestPassCount As Integer
Dim TestFailCount As Integer
TitleId = 4
'TestPassCount = 0
'TestFailCount = 0

'Retrieve number of records in the TestData SpreadSheet
Dim TestDataRowCount As Integer
TestDataRowCount = Worksheets("TestData").UsedRange.Rows.Count

If (TestDataRowCount <= 2) Then
  MsgBox "No records to validate.Please provide test data in Test Data SpreadSheet"
Else
  For RecordId = 3 To TestDataRowCount
    RefreshResultSheet
    'Source File row count
    SrceFile = Worksheets("TestData").Range("D" & RecordId).Value
    Set sourcewb = Workbooks.Open(SrceFile)
    With sourcewb.Worksheets(1)
      SourceRowCount = .Cells(.Rows.Count, "A").End(xlUp).Row
      sourcewb.Close
    End With

    'Target File row count
    TrgtFile = Worksheets("TestData").Range("E" & RecordId).Value
    Set targetwb = Workbooks.Open(TrgtFile)
    With targetwb.Worksheets(1)
      TargetRowCount = .Cells(.Rows.Count, "A").End(xlUp).Row
      targetwb.Close
    End With

    ' Set Result Test data value
    TitleId = TitleId + 3
    Worksheets("Result").Range("A" & TitleId).Value = Worksheets("TestData").Range("A" & RecordId).Value

    'Compare Source and Target Row count
    Resultid = TitleId + 1
    Worksheets("Result").Range("A" & Resultid).Value = "Source and Target record Count"
    If (SourceRowCount = TargetRowCount) Then
       Worksheets("Result").Range("B" & Resultid).Value = "Passed"
       TestPassCount = TestPassCount + 1
    Else
      Worksheets("Result").Range("B" & Resultid).Value = "Failed"
      TestFailCount = TestFailCount + 1
    End If
  Next RecordId
End If
UpdateTestExecData TestPassCount, TestFailCount
End Sub

Sub RefreshResultSheet()
  Worksheets("Result").Activate
  Worksheets("Result").Range("B1:B4").Select
  Selection.ClearContents
  Worksheets("Result").Range("D1:D4").Select
  Selection.ClearContents
  Worksheets("Result").Range("B1").Value = Worksheets("Instructions").Range("D3").Value
  Worksheets("Result").Range("B2").Value = Worksheets("Instructions").Range("D4").Value
  Worksheets("Result").Range("B3").Value = Worksheets("Instructions").Range("D6").Value
  Worksheets("Result").Range("B4").Value = Worksheets("Instructions").Range("D5").Value
End Sub

Sub UpdateTestExecData(TestPassCount As Integer, TestFailCount As Integer)
  Worksheets("Result").Range("D1").Value = TestPassCount + TestFailCount
  Worksheets("Result").Range("D2").Value = TestPassCount
  Worksheets("Result").Range("D3").Value = TestFailCount
  Worksheets("Result").Range("D4").Value = ((TestPassCount + TestFailCount) / TestPassCount)
End Sub