Hope this helps to get you started.
Code:
Dim objmap As MapPointCtl.Map
Set objmap = MappointControl1.ActiveMap
Dim aShape As MapPointCtl.Shape
Dim aPushpin As MapPointCtl.Pushpin
Dim bPushpin As MapPointCtl.Pushpin
Set aPushpin = objmap.AddPushpin(objmap.FindResults("New York, NY").Item(1))
Set bPushpin = objmap.AddPushpin(objmap.FindResults("Atlanta, GA").Item(1))
Set aShape = objmap.Shapes.AddLine(aPushpin.Location, bPushpin.Location)
aShape.Line.BeginArrowhead = False
aShape.Line.EndArrowhead = True
aShape.Line.Weight = 7
aShape.Line.ForeColor = vbBlue
Set aPushpin = objmap.AddPushpin(objmap.FindResults("Chicago, IL").Item(1))
Set bPushpin = objmap.AddPushpin(objmap.FindResults("Denver, CO").Item(1))
Set aShape = objmap.Shapes.AddLine(aPushpin.Location, bPushpin.Location)
aShape.Line.BeginArrowhead = False
aShape.Line.EndArrowhead = True
aShape.Line.Weight = 10
aShape.Line.ForeColor = vbGreen
Set aPushpin = objmap.AddPushpin(objmap.FindResults("Denver, CO").Item(1))
Set bPushpin = objmap.AddPushpin(objmap.FindResults("New York, NY").Item(1))
Set aShape = objmap.Shapes.AddLine(aPushpin.Location, bPushpin.Location)
aShape.Line.BeginArrowhead = False
aShape.Line.EndArrowhead = True
aShape.Line.Weight = 2
aShape.Line.ForeColor = vbRed