The fitted value at time t is the smoothed value at time t – 1. The forecasts are the fitted value at the forecast origin. If you forecast 10 time units ahead, the forecasted value for each time will be the fitted value at the origin. Data up to the origin are used for the smoothing.
In naive forecasting, the forecast for time t is the data value at time t – 1. Perform single exponential smoothing with a weight of one to perform naive forecasting.