DynamicModule[{inputData = 0, dataSet = {}},
 Column[{Dynamic[{dataSet}],
   InputField[Dynamic[inputData]],
   Button["Plot",
    AppendTo[dataSet, Table[inputData + i^j, {i, 5}, {j, 2}]]],
   Spacer[5],
   Dynamic@ListPlot[dataSet, Joined -> True, ImageSize -> {300}]
   }]]