You can add a new line to a text string by including vbCrLf in the string.

Plot.Shapes.AddText("line1" & vbCrLf & "line2") 

The vbCrLf constant consists of a carriage return Chr(13) and a line feed Chr(10). For more information about Visual Basic string constants, refer to the BASIC Language Help accessed from the Scripter Help menu. 

Sub Main
    Dim SurferApp, Plot, Text, FontFormat As Object
    Set SurferApp = CreateObject("Surfer.Application")
    SurferApp.Visible=True

    Set Plot = SurferApp.Documents.Add

    Set Text = Plot.Shapes.AddText(5,7, "This is my text"& vbCrLf & "This is my text on the second line")

    Set FontFormat = Text.Font
    FontFormat.HAlign = srfTACenter
End Sub

Updated November 1, 2018