Trains run frequently from, for instance, Barcelona to the BCN Airport. You can see a timetable by selecting the "Barcelona to BCN Airport and v.v." link. When the RENFE page opens, select "Horarios" (timetables) to see a page like the one illustrated here. This is an example of how to use it. 

The circled numbers, 1, 2, 3, 4 on the sample page relate to the steps below

1. Click on the 'Origen' field to select BARCELONA or any other offered departure station
(click on the black downward pointing arrowhead at the right-hand end of the field where you see BARCELONA SANTS)

2. Click on the 'Destino' field to select AIRPORT or any other offered destination station

3. You can select a Fecha (particular date) or a tipo dia (type of day)
Domingo (Sunday) Lunes (Monday), Laborales (Work Day) etc.

4. Then click on the Horarios symbol to get a timetable of the day's trains