There is the ParcelMap sample in the standard sample, it demonstrates how to search by a field value in the layer and zoom into the found feature.
dim layer as Layer = map("shapefilename")
dim rs as Recordset = layer.SearchExpression("FIELDNAME = """ & fieldvalue & """")
if Not rs.EOF then
map.Extent = rs.RecordExtent
' or map.ZoomScale(rs.Shape.Centroid, 100000)